What is a good introductory book on quantum mechanics? I'm really interested in quantum theory and would like to learn all that I can about it. I've followed a few tutorials and read a few books but none satisfied me completely. I'm looking for introductions for beginners which do not depend heavily on linear algebra or calculus, or which provide a soft introduction for the requisite mathematics as they go along.
What are good introductory guides to QM along these lines?
 A: I am a great fan of Albert Messiah, 'Quantum Mechanics', now available (two volumes bound as one) in a sturdy paperback from Dover, at reasonable cost.
Don't know why this has dropped out of fashion-- people complain it is too much oriented towards nuclear physics.  Well I am a physical biochemist turned magnetic resonance jock, and I find it excellently adapted to my needs.
The problem here is that there are no easy good books.  The subject is intrinsically hard.  Earlier responders cited Landau and Dirac; Landau is another favorite of mine, but harder than granite-- Dirac is brilliant but legendary for difficulty.  Reading Dirac is like trying to climb a sheer marble wall-- footholds and handholds are not abundant.  Landau (at least) often gives a good physical reason why such and such thing should be so, before he starts writing equations.  Be prepared to spend much time meditating on his meaning.
Good luck.
A: Introduction to Quantum Mechanics by David Griffiths, any day! Just pick up this book once and try reading it. Since you have no prior background, this is the book to start with. It is aimed at students who have a solid background in basic calculus, but assumes very little background material besides it: A lot of linear algebra is introduced in an essentially self-contained way.
Furthermore, it contains all the essential basic material and examples such as the harmonic oscillator, hydrogen atom, etc. The second half of the book is dedicated to perturbation theory. For freshmen or second-year students this a pretty good place to start learning about QM, although some of the other answers to this question suggest books that go a bit further, or proceed at a more rigorous level.
A: I think, perhaps with all the above book recommendations you could also try following a proper online quantum mechanics course. I know two such excellent courses that might be of interest.


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*Quantum Physics by V.Balakrishnan. The instructor introduces all the basics of linear algebra you need, But you will have to work very hard On your own because he will also introduce a lot of other fancy math that you might need(for instance he will speak about L^2- spaces.)
I do not know a proper book that goes along with the course (Other's might recommend that)
NOTE: I checked out R.Shankar's Book "Principal's of quantum mechanics". It goes pretty well with the above online course. 

*Quantum Physics By JJ Binney. This is also a very nice introductory course taught to undergraduate students at Oxford. This might be something that will help you a lot. The book that goes along with the course is also available by the same author (free of cost) here.

*Although there are tons of lecture notes available online. I found this to be extremely useful.

*The QM course by Alan Adams in MIT is very very awesom.IMHO,he is the best teacher .Best part in it is that he inspires the students to ask questions and the MIT students ask so many good questions,that also helps the person who is watching the video lectures.
In the site you will also find books that goes along with the course.
http://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2013/
A: *

*A book for self study to get you from introductory QM to elementary is Claude Cohen-Tannoudji's Quantum mechanics textbook which is in two volumes. It has a very high price but it deserves it. It has all the glory details inside! (Shankar's book is also great and is on the same level and also covers path integrals. Griffiths' is only introductory, although it also has some chapters that other books on the same level do not have)

*One for introductory to elementary QM is Zettili's Quantum Mechanics: Concepts and Applications. It also contains a lot of exercises in it and many solved problems.

*For mastering the knowledge gained in the above books, a problem solving book is recommended (both Amazon links):


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*Galitski et al Exploring Quantum Mechanics:  A Collection of 700+ Solved Problems for Students, Lecturers, and Researchers

*Lim's Problems and Solutions on Quantum Mechanics
These books will be with you from this level to a PhD level. Very useful books. And except for only using them to master the things that the above books have taught you, you will find them to be very useful for mastering stuff from more advanced textbooks (graduate and advanced undergraduate).
A: For quantum mechanics, the original is still the best:


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*Dirac's "The Principles of Quantum Mechanics".


It's clear, it's terse, and it's comprehensive. All other books take most of their material from this source.
For a basic short introduction to quantum mechanics, you can't beat:


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*Feynman Lectures on Physics Vol III
This is very good and intuitive, and complementary to the remaining books.


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*Landau and Lifschitz "Quantum Mechanics"


is heavy on good exercizes and mathematical tools. L&L include topics not covered everywhere else. The standard undergraduate books on quantum mechanics are not very good in comparison to these, and should not be used.
A book which requires minimum of calculus or continuous mathematics is 


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*Nielsen & Chuang: "Quantum Computation and Quantum Information"


This focuses on modern research, and discrete systems in quantum computation. If you don't know calculus, learn it, but you might find this book the most accessible. It's long though.
On advanced quantum mechanics, there are good books are by Gottfried and by Sakurai. Berezin's book is also a great classic.
For the path integral, you can read Feynman and Hibbs, but I like Feynman's 1948 Reviews of Modern Physics article more. There is also a good book which covers the path integral:


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*Yourgrau & Mandelstam: Variational Principles in Classical and Quantum Physics.


The original source for the Fermionic path integral is still the best, in my opinion:


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*D.J. Candlin: Il Nuovo Cimento 4 no. 2, 231 (1956)
If you want to convince youself quantum mechanics is necessary, you should recapitulate the historical development. For this, the following source is good:


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*Ter Haar's "The Old Quantum Theory" (it's short) to learn Bohr Sommerfeld quantization


You can also read the Wikipedia page on old quantum theory for a sketchy summary, then look at the page on matrix mechanics. This explains the intuition Heisenberg had about matrix elements, something which is not in Dirac's book or anywhere else. Heisenberg's reasoning is also found to certain extent in the first chapters of this book:


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*Connes "Noncommutative geometry".


This book is also very interesting for other reasons.
A: For the begining you can start with Quantum Mechanics for Engineers - Leon van Dommelen, its available freely on the author's site:
http://www.eng.fsu.edu/~dommelen/quantum/style_a/index.html
Let the author speak for himself:

Here you will find the same story as physicists tell there own
  students. The difference is that this book is designed to be much
  easier to read and understand than comparable texts. Quantum mechanics
  is inherently mathematical, and this book explains it fully. But the
  mathematics is only covered to the extent that it provides insight in
  quantum mechanics. This is not a book for developing your skills in
  clever mathematical manipul­ations that have absolutely nothing to do
  with physical under­standing. You can find many other texts like that
  already, if that is your goal.

A: I would suggest "Quantum physics of atoms, molecules, solids, nuclei, and particles" by Robert Martin Eisberg, Robert Resnick, if you want to have very good understanding without sophisticated mathematics. With emphasis on applications ,the authors discussed every topics with physical insigth, without much more mathematics (but need to know some basic calculus).The book explains you how microspcoic world works.
A: Quantum Mechanics in Simple Matrix Form: [Amazon link]
No calculus is found in this book. All concepts in linear algebra are introduced. Unfortunately, this means you won't encounter stuff like the Schrodinger equation. You will have a much better than PBS understanding of quantum mechanics (what is quantum state, how you can add states, probability in quantum mech, etc.). Lightweight and cheap!
A: *

*Mark Beck, Quantum Mechanics: Theory and Experiment, might be the best QM book there is. The math needed is modest, but knowledge of optics and electromagnetic waves is almost necessary. 


You can also try two simpler, very short books by Valerio Scarani (aimed at, mainly, high school students), 


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*Quantum Physics: A First Encounter: Interference, Entanglement, and Reality 

*Six Quantum Pieces: A First Course in Quantum Physics. 


All three books are modern: instead of stressing (otherwise free) particle(s) in a box and the Bohr's atom, they emphasize one particle interference, entanglement, local realism, quantum teleportation. Dr. Beck's book describes quantum optics labs that his undergraduate students really performed, to test single-photon interference, violation of local realism, etc. 
Another modern book is 


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*Exploring the Quantum by Serge Haroche and Jean-Michel Raimond. 


It's at about the difficulty level of Mark Beck's book, but much cheaper when buying it used. Similar to Valerio Scarani's books are 


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*Dance of the photons by Anton Zeilinger, and 

*Quantum Enigma by Bruce Rosenblum and Fred Kuttner. 


Note that all the above authors are well known professors and/or researchers.
A: Many recommendations have already been made. I would just like to recommend Principles of Quantum Mechanics by Ramamurti Shankar.
I like this book because it starts with all necessary algebra, then goes into operator formulation of classical needed in quantum, and then into quantum.
I would recommend it over Griffiths for a person who is not great at linear algebra and is at the preliminary level. After that Griffiths is fine.
A: OK.
First, you need a some comfort in Linear Algebra.
Go to the MIT Open Courseware site and watch the Linear Algebra lecture (videos) by Strang. These are great.
Next, watch the "Theorectical Minimum" videos by Leonard Susskind .  They represent the theoretical minimum that you need to know about quantum mechanics. (i.e. the title of the video course is theoretical minimum, but it is in fact a course on quantum mechanics.    Susskind is a great teacher and the videos are great.  You can access them on itunes and You Tube.  Search for Susskind lectures quantum mechanic from Stanford.  They are just released (a few weeks ago)
Finally, the text you want is Principles of Quantum Mechanics by Shankar.  He is also a great teacher.   He does have some video lectures on general physics, but he does not have a video lecture on Quantum Mechanics.  Nonetheless, his book is a great book for learning.  It is about $70, but if you google around (with PDF in your google search) you may get lucky.
A: If you're new to this, start with University Physics by Young and Freedman. The reason is that this book discusses the concepts without the rigorous math.
Study the following chapters:
Chapter 38 Photons: Light Waves Behaving as Particles
Chapter 39 Particles Behaving as Waves
Chapter 40 Quantum Mechanics
Chapter 41 Atomic Structure
Chapters 38 and 39 give you background of early quantum theory. Chapter 40 and 41 discusses quantum mechanics.
You can also read Feynman Lectures Volume 3 to grasp the concepts without heavy math.
If you want to dig deeper, you have to study linear/matrix algebra and calculus. Afterwards, read Introduction to Quantum Mechanics by David Griffiths or Richard Liboff.
Then if you want more, read Modern Quantum Mechanics by J.J. Sakurai.
That's how I suggest you do it. Quantum Mechanics is, unfortunately, on of the more difficult physics subjects. You have to build you knowledge from easier texts or else you will get lost.
Watching lectures is also an option. Stanford and Oxford uploaded their QM lectures in Youtube. Then again, you have to know calculus and linear algebra to be able to keep up with the lectures.
Cheers!
Berty
A: Feynman's Six Easy Pieces is an excellent introduction to quantum mechanics. For a more thorough analysis (and some philosophical ruminations), I'd recommend The Dancing Wu Li Masters by Gary Zukav. For an easy-to-understand discussion of the weirdness of quantum mechanics, Fred Kuttner and Bruce Rosenblum's Quantum Enigma: Physics Encounters Consciousness is excellent. 
Here's an Amazon list I put together with some books I've found helpful.


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*Robert Kroese, author of Schrödinger's Gat
A: A quantum mechanics primer by Gillespie is good. Is only 125 pages long. It starts covering the basic mathematical tools from the ground: probability, complex numbers, vectors, operators in Hilbert space, and a review of classical mechanics including the Hamilton formulation. Then goes through the quantum mechanics postulates with simple, yet accurate math. It uses a notation slightly different from the Dirac bra-ket notation but it is in essence the same, perhaps more readable for newbies.
The main strong point is that it does not suppose any previous knowledge but basic calculus, and yet it gives a reasonable understanding of the basic formalism and its meaning.
I think it is a perfect companion for other books, as Griffith or Shankar.
This is a review https://doi.org/10.1119/1.1987211
A: If you are not willing to learn the linear algebra upon which the entire theory of quantum mechanics is based, then you really aren't going to have much luck finding the kind of textbook you seek.  It sounds to me like what you want is a textbook that introduces you to what is called "modern physics" instead.  Most "modern physics" texts cover quantum mechanics concepts while remaining mostly in algebra land.  Most of the textbooks recommended in the answers posted before mine are chock full of calculus.
Learning how to multiply matrices and vectors isn't hard at all -- you can learn it from a Wiki, from YouTube, or Khan Academy.  Once you know how to do that, I strongly recommend the first few chapters of the following textbook:
"Quantum Mechanics : A Paradigms Approach", by David H. McIntyre
I used this book the last time I taught quantum mechanics, and the students really liked it a lot.  You can teach yourself "real" quantum mechanics from this book using the Dirac bra-ket notation used in real physics research and in quantum information theory.
Once you learn calculus, you can tackle any of the other books recommended by other answers, but my personal favorite -- which would prepare you for graduate work in quantum theory -- is
"A Modern Approach to Quantum Mechanics", by John S. Townsend.
I used to use Griffiths' text due to its popularity and the due to the traditional stress on the wave function.  However, my students did not get as much out of the Griffiths' text as they do from the two I mentioned above.  Furthermore, I am now convinced that students are better served by learning the state-vector approach instead of focusing solely on the wave function, as it allows them to read recent papers about breakthroughs in QM research.  You can't do too much with wave functions when your experiment deals with particle spins or with photon polarizations.
A: Quantum mechanics is a rather rich-in-concept subject which you cannot learn from a single book. So in this answer I am providing a list of the books on the subject that I found to be useful in understanding the quantum world.


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*Principles of Quantum Mechanics (Dirac): A classic text by Dirac. Though the notation is old-fashioned, yet the best one to learn the conceptual ideas. Anyone reading at least the first chapter of this book should develop a love for the subject.

*Quantum Mechanics (Landau): Another classic text. It is terse, comprehensive and heavy on exercises, but discusses topics that are not usually contained in other standard textbooks.

*Quantum Mechanics (Cohen-Tannoudji): A comprehensive graduate level reference in two volumes. It is well written and discusses many useful applications.

*Feynman Lectures (Volume-3): This one surely needs no introduction. A classic text that is heavy on concepts along with Feynman's insightful discusions. A must read for everyone interested in quantum mechanics.

*Quantum Mechanics (Shankar): An introductory level text that starts with a discussion on necessary algebra. Shankar's explanations are quite different but elegant compared to other authors. This also includes discussion on path integrals.

*Quantum Mechanics (Messiah): A classic, comprehensive text in two volumes. The notation is old fashioned but the elegant explanations makes it a must-read even today.

*Quantum Mechanics: A modern introduction (Das and Melissinos): A well written text suitable for undergraduates. The discussion of Scattering Theory is the best part of the book.

*A Modern Approach to Quantum Mechanics (Townsend): A comprehensive graduate level text that covers almost everything of a graduate course in quantum mechanics. But linear algebra is a prerequisite for this textbook.

*Modern Quantum Mechanics (Sakurai): A comprehensive and modern introduction to quantum mechanics suitable for graduates. It also contains a rich collection of problem.

*Lectures on Quantum Mechanics (Weinberg): An advanced level text suitable for graduate level that discusses many important discussion which are not usually found elsewhere.

A: There is an excellent book called "The Road to Reality" by Roger Penrose.  It is an interesting mix, being written in a conversational, easy going and accessible way, with brilliant and insightful descriptions from a real master of the craft.  However, it does not skimp on the mathematics.  If you are serious about exploring quantum mechanics, and fundamental physics more generally, this great place to look. It is a fun, though not so easy, ride.
A: If you want to do more than "just calculate" (as either Feynman or N David Mermin once might have said searching for the origin of the famous quote ) one of the best ways to flesh out your insight into quantum physics, IMO, is the recent, short and very readable "Beyond Weird - Why everything you thought you knew about quantum physics is different" by Philip Ball (an editor of the journal Nature). Even some profs of theoretical physics have acknowledged that it was the book they wished they themselves had written.
He gets to grips with the niggling questions that always arise as you start working through the subject and I've found him particularly good on decoherence and the measurement problem. 
He's clearly thought deeply about the subject over a long time and his editorial experience gives him the edge in explaining difficulties that calculators gloss over without a second thought.
I think it's a great adjunct to any introductory course in QM and should be on reading lists.
It's available on Kindle (cheaper in the US than the UK right now 01/01/19)
https://www.amazon.com/Philip-Ball/e/B001H6P9SO/ref=sr_tc_2_0?qid=1546371784&sr=1-2-ent
A: Best introductory books

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*Zettili, Nouredine (2009). Quantum Mechanics: Concepts and Applications (2nd ed.). Chichester, UK: Wiley. ISBN 978-0470026793.

This is a very good book and is easily understandable. It has nice notations and is very formal. The author likes to write every statement as general as possible (which is usually seen in advanced comprehensive books but not in introductory books). It looks like this book is gaining popularity as an alternative to Griffiths book for UGs. Like Griffiths, it contains a lot of exercises in it and many solved problems.


*Griffiths, David; Schroeter, Darrell (2018). Introduction to Quantum Mechanics (3rd ed.). Cambridge University Press.

The most popular introductory QM textbook. Good for intuitive understanding for beginners. You probably already know about this book, so I am not going to discuss much about this.


*Shankar, Ramamurti (2011). Principles of Quantum Mechanics (2nd ed.). Plenum Press. ISBN 978-0306447907.

This book is fairly rigorous but still feels like a very intuitive pedagogical approach. It is written for grad students unlike the above 2, but it still is very readable for UGs.


*Sakurai, J. J.; Napolitano, Jim (2017). Modern Quantum Mechanics (2nd ed.). Cambridge University Press. ISBN 978-1-108-42241-3.

This book is at a similar level to Shankar. But is somewhat smaller, so the explanations are somewhat shorter. It still is a very good book.
Note: The last 2 books also discuss introduction to relativistic quantum mechanics.
