What are good books for graduates/undergraduates in Astrophysics? There are no book recommendations for Astrophysics here. I will write my own answer, but I am also interested in what are others' views on the question (I will NOT mark my own answer as the best one).
 A: In my experience, few astrophysics books stand out as being particularly excellent. For anyone just starting who wants a broad, easy overview


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*An Introduction to Modern Astrophysics by Carroll and Ostlie


is the classic, mostly for its comprehensiveness. Don't expect anything high level - undergraduates majoring in astro should quickly find themselves beyond the level of the book - but it offers a brief introduction to almost everything, and can serve as a unified handy reference for all those bizarre conventions astronomers use.
For one specific topic, however, I can think of an excellent book. I have never seen stellar theory presented better than in


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*Structure and Evolution of the Stars by Martin Schwarzschild


(no longer in print). All of the important concepts are presented in a natural way. Reading the whole book cover-to-cover took two evenings, after which stellar theory seemed natural and easy. Of course, for modern research one should be aware that most of Schwarzschild's numbers are off - experimentally obtained opacities and nuclear rates were prone to error back then - and there are more nuances that have since been explored.
A: The two books on my shelf that I regularly thumb through are:


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*Galactic Dynamics by Binney and Tremaine

*Galaxy Formation and Evolution by Mo, van den Bosch and White


You can probably tell from the titles that neither is a general astronomy text. I find both to be excellent graduate-level texts on their topics. Galactic Dynamics is a classic from the '70s, but was thoroughly revised into a second edition in 2008. It covers nearly everything one could want to know about orbits in general potentials, including both collision-less and collisional fluids, and a wealth of applications to galactic systems. I like Galaxy Formation and Evolution because it is modern (2010), which I think is important for a field that is changing so rapidly. It covers a lot of ground, both processes internal to galaxies and interactions with their surroundings and the broader cosmological environment. 
I'll also add another mention for:


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*An Introduction to Modern Astrophysics by Carroll and Ostlie


As others have mentioned, it is a broad overview. I recall it being easy to read. Now I use it occasionally for reference on topics outside of my particular field (for which I have more detailed books).
A: The books listed in the previous posts range from "pretty easy" to "extremely hard"...... so it all depends on your learning goals:


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*achieving a general understanding?

*acquiring detailed physical knowledge?

*sophisticated expert knowledge?
If you go for the simplest introductory texts, then you will sacrifice some of the necessary rigour and breadth, and the oversimplifications will probably hinder your path onwards towards true expert knowledge. On the other hand, physical understanding can be achieved without necessarily reading texts in which every page is filled with equations!
So I here review some relatively-easy physical/mathematical introductory texts that do not sacrifice scholarly rigour......
Here is a list of relatively easy (but rigorous) "introductory-to-intermediate level" books on Stellar Evolution & Stellar Structure, with the readership level of the individual books somewhere within the range of "lower undergraduate" through to "easy graduate texts". In other words, in these books you can expect to find graphs and algebra (but not millions of equations from cover to cover!) plus a modest amount of calculus, though with the maths and physics leavened with substantial amounts of descriptive material. 
These books are are easily understandable only if the reader has already studied a good year of rigorous maths (especially a Calculus & Analytic Geometry course) and physics at the tertiary level. 
However, those who have studied the odd unit of maths and physics, and who are familiar with detailed physical/scientific argument,  will be able to understand the easier sections of these books if they have enough mathematics to be confident about:


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*algebra 

*the graphical display of functions and relations between variables

*elementary calculus and differential equations (desirable)
BOOK REVIEWS: (texts on stellar evolution and stellar astrophysics)
"Stars and Stellar Evolution", by K.S. de Boer and W. Seggewiss, 2008, ISBN 9782759803569
An excellent concise primer on stellar evolution. All the observational facts are here,  but without bogging the reader down in the recondite physics of stellar interiors.  This terse volume somewhat resembles an excellent set of university lecture notes, but it is also greatly padded out with ALL of the necessary details. It is not too maths heavy , and contains megatons of useful stellar data and HR diagrams! The good thing about this book is that it presents the intricate and non-simplified details of how various types of stars evolve, but mainly in terms of the Observables and their functional relations.....for instance: surface temperature, stellar mass, stellar luminosity, Color-magnitude diagrams, SEDs and spectra.  The necessary equations are there, but the pages of this book are not loaded with complex physics and mathematics. Mind you, if you are only used to descriptive books on astronomy, it is still very far from being an easy read. 
"The Life and Death of Stars", 2014, by Ganesan Srinavasan, Springer-Verlag, ISBN 9783642453847    
I really like this book.....as I can easily understand the physics and maths in it (My mathematics is OK, but I am no mathematician as my maths is still stuck at the mid-undergraduate university level). This is one of the easiest-to-read undergraduate-level courses in stellar evolution, and it is very understandable, as the physics and maths is pared down to the necessary minimum. Srinavasan says that he only assumes that you understand physics at about first-year university level, e.g. that you have understood the likes of "Halliday and Resnick". 
However, the author's somewhat simplified approach to the necessary physics and mathematics does not sacrifice scholarly rigour and sophistication; in this respect, Srinavasan's book is markedly superior to a lot of the other introductory (early undergraduate) astrophysics books,  which are too often oversimplified to the extent that the simple level of the exposition hinders the future progress of the student's understanding. 
"Unsolved Problems in Stellar Evolution", 2000, edited by M.Livio, Cambridge University Press, ISBN 0521780918  
An excellent course in the basics of stellar evolution, without any over-simplification. Quite a lot of the text is descriptive, but the text is complex and physical in orientation, and it is fundamentally very highbrow and "technical" in content. 
It mainly uses graphs rather than equations to display numerical relations, so this makes it relatively accessible, even for super-advanced amateur astronomers and for undergraduates in the physical sciences.
See madbadgalaxyman's review of this book at (American) amazon.com
"Introduction to the Theory of Stellar Structure and Evolution", 2010/2011, 2nd edn, by Dina Prialnik, Cambridge University Press, ISBN 9780521866040
 .
This book is a well-regarded textbook on the physical theory of stellar interiors, here reduced to its basics.....but even the basic physics of stellar interiors is still hard (unless you are very conversant with physics!).
"Evolution of Stars and Stellar Populations",  2005 , by Salaris and Cassisi, John Wiley & Sons, ISBN: 9780470092200
An essential reference for the intermediate-to-advanced student of stellar astronomy, describing the modern approach to stellar evolution. The sophisticated exposition in this book stands in marked contrast to the often out-of-date and/or oversimplified material found in many lower-undergraduate astronomy textbooks. At least Seventy percent of this book sticks to observables such as Color-Magnitude diagrams, graphs of scaling relations, and spectra. While this book is usually regarded as a "graduate level" or "beginning professional astronomer" text, this work is so clear and observationally-oriented that the resolute physics/maths undergraduate or the Super-Advanced Amateur Astronomer can (at least with some struggle!) understand large sections of it. 
See madbadgalaxyman's review of this book at (American) amazon.com. 
"Stellar Spectral Classification", 2009, by Richard O. Gray and Christopher J. Corbally, Princeton Series in Astrophysics, Princeton University Press, ISBN 9780691125114
This book is literally "The Bible" of stellar spectra and stellar spectral classification. This massive and comprehensive and scholarly work is an essential reference for all optical and near-infrared astronomers. This book explains the current iteration of the standard MK System of Classification of the spectra of stars, and it contains a comprehensive collection of stellar spectra , with detailed explanatory information on the many stellar types, including spectra and explanations of most of the recently-discovered stellar and sub-stellar types (e.g. the L & T dwarf classes, and brown dwarfs). Extreme and rare stars like O2/O3 stars and Wolf-Rayets and LBVs also get a much greater coverage than in earlier references, reflecting today's greater knowledge of these "superstars". This work somewhat resembles a supercharged and super-extended version of Kaler's popular-level book on Stellar Spectra.....and it is much more up-to-date! Because the Spectral Classification of Stars does not have to involve lots of hairy physics and mathematics, this is an area of professional astronomy in which amateur astronomers can become highly competent. 
"An Introduction to Modern Stellar Astrophysics" by Dale A. Ostlie and Bradley W. Carroll
I have this book, but I have only read 30 percent of it, so I am unsure as yet if I can recommend it. This tentative review records my initial impressions of this work.
This is a "basic to early-intermediate level" quantitative/numerical/physical textbook on stellar structure and evolution, at the undergraduate level. In other words, it assumes an absolute minimum of a good Australian Year 12 advanced maths & physics, though in reality a good First Year University maths and physics would be better preparation for the reader. Mercifully, there is also significant descriptive material to leaven the equations.
At face value, this is a typical "American textbook -style" introduction to the basics of stellar astrophysics, and it is suitable for people with a physics/maths orientation;  in other words, suitable for those people who are comfortable with equations and graphs and who have done at least an introductory calculus course (with a few differential equations).  The authors write: "Our goal in writing this book was to open the field of modern astrophysics to the reader by using only the basic tools of physics". Those sections that I have read engage in the maximum amount of 'handholding' for the reader, and the authors explain astrophysics in a style and simplicity which makes it (hopefully) accessible to the numerate "everyman" who has at least some physics and maths. 
The mathematics and physics and the arguments are indeed simplified and reduced to their absolute essentials.....which has the significant drawback that if the reader wants to go further and eventually to become a senior-undergraduate to graduate Level astrophysicist, he/she will have to restudy these topics in much greater breadth and detail. In summary, Ostlie and Carroll are bravely attempting to "gently ease the reader into" the inevitably difficult field of astrophysics!

A: This depends on your purpose. You may be planning to study a single text from the first page up to the back cover, to get a good idea of nowadays astrophysics across different fields, without entering in very detailed phenomenology. In that case, this is a good choice:


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*Astrophysics for Physicists, by Arnab Rai Choudhuri, 2012 Cambridge University Press


This is a compact book, focusing on physical principles rather than phenomenological descriptions. As nearly all general texts, it introduces cosmology from a Newtonian scheme, but then it adds two optional chapters on GR and relativistic cosmology. That is one strong point, as opposed to similar literature in the field. It may be, however, very short in some specific areas (or simply not cover them).
But if your purpose is having a more comprehensive reference, suitable for selecting only the topics you need, here is a combination of two excellent books:


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*An Introduction to Modern Stellar Astrophysics, by Bradley W. Carroll & Dale A. Ostlie, Addison-Wesley

*Extragalactic Astronomy and Cosmology, by Peter Schneider, 2006 Springer
They are complementary in its scope. The first one has one of its strongest points in the description of stellar structure and evolution, where it is very clear and full of details, althogh it puts less weight on describing the underlying physics than Choudhuri. It comes with some example codes in fortran and c. The second one is a gem for extragalactic astronomy with a comprehensive coverage, from a very authoritative researcher on gravitational lensing.
Beware of a book called 'An Introduction to Modern Astrophysics', by Carroll/Ostlie too. It is simply the same excellent book on stellar physics, put together with an independent second part that is not as good as the first. The resulting creature is a 1300 pages monster, with extremely small left inner margins that make some chapters almost physically impossible to read.
And finally, some books try to offer a very wide coverage of topics, while restricting the mathematics to a minimum. They are a nice read for beginning undergrads or serious amateurs. One of them is:


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*Introductory Astronomy and Astrophysics, by Michael Zeilik & Stephen A. Gregory
A: My favor introductory book is no doubt:


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*The Physical Universe: An Introduction to Astronomy -Frank Shu


It introduces astrophysics in an inspiring way; it also contains beautifully written introduction to key physics needed. However, as a book with age, it is in lack of modern topics. 
A: The answers and book suggestions already posted are pretty good, I own a couple of those books already.  However, if a person is just starting out in their study of Astrophysics and needs to learn more than everyday common knowledge of the Universe, the book Welcome To The Universe By Neil deGrasse Tyson, J. Richard Gott, and Michael A. Strauss does a very good job of covering the overall scope of the Astrophysics topics in a very entertaining way.  It is a bit more than easy armchair reader as I did have to get out paper and pen to go thru a few of the equations included for clarification.  However, this is not a study text, more of a "firing up the enthusiasm" for a deeper study.
Also for a deeper dive study (undergraduate level) I submit An Introduction to Modern Astrophysics by Bradley W. Carroll and Dale A. Ostlie.  This book is a fairly good all-inclusive text to pick up on the broad scope of Astrophysics.  I have the second edition, copyright 2007, and there is a newer publication, 2017, of this book but it is the same edition but different publishing house.
A: For undergraduates Introduction to Particle and Astroparticle Physics - Multimessenger Astronomy and its Particle Physics Foundations | Alessandro De Angelis | Springer provides an introduction to astrophysics and cosmologt with emphasis on multimessenger astronomy (gravitational waves and neutrinos)
