What are some of the best books on complex systems and emergence? I'm rather interested in getting my feet wet at the interface of complex systems and emergence. Can anybody give me references to some good books on these topics? I'm looking for very introductory technical books. 
 A: Maybe these three lectures about emergence could be interesting to get a first overview of the topic. Therein Prof. De Deo explains for example that emergence has a lot to to with what new phenomena can occurre when coarse graining (or renormalizing) microscopic degrees of freedom of a large system to obtain an effective (possibly including emergent phenomena) macroscopic description. 
Background material to understand and deepen the wisdom about the concepts presented in these lectures can be found here. Among these resources is this book titled "Statistical Physics: Statics, Dynamics and Renormalization". It explains not only the statistical mechanics basics, but from the authors "interdisciplinery" point of view it includes topics such as renormalization, self-organized criticality complexity, and other things which are useful and important to understand emergence (as explained in the video lectures). 
I've just read some chapters of this book, it is slightly technical and very accessible, and the style of writing makes me wanting to read the whole thing.
A: I like the book Energy Landscapes by David Wales. It deals with various classes of complex systems (clusters, glasses, proteins) in the context of chemistry.
I want to add - emergence is fraught with flaky ideas; a lot of appeals to ignorance are rooted from the idea of irreducible complexity. So because we can't, say, predict the weather from $F=ma$, this means that God makes it happen.
If you're interested in something "bigger" than the chemistry of complex systems, I like the work of David Bohn (say, The Undivided Universe).
A: An Introduction to Complex Systems is a recently published (2019) book by Tranquillo that has been very well reviewed in the Nov. 2019 Physics Today issue:

The text provides a useful overview of complex systems, with enough detail to allow a reader unfamiliar with the topic to understand the basics. The book stands out for its comprehensiveness and approachability. It will be particularly useful as a text for introductory physics courses.
  [...]
  Tranquillo has written a thorough textbook that gives a useful introduction to complex adaptive systems as a whole field. It can also serve as a quick reference for seasoned practitioners who need a refresher on a particular subject.

Which also points out that:

math is well-integrated into the text, a reader could skim over the equations and focus instead on the prose without losing much. Tranquillo’s presentation will allow math-phobes to be slowly exposed to equations—alongside good explanations—without being forced to read through proofs line by line; thus the book is a useful text for mixed-population undergraduate courses.

Which seems to make it fit very well into the "very introductory technical books" category.
A: 
This answer contains some additional resources that may be useful. Please note that answers which simply list resources but provide no details are strongly discouraged by the site's policy on resource recommendation questions. This answer is left here to contain additional links that do not yet have commentary.



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*James P. Sethna is one of the leading figure in this area.
You can refer to his book without any doubt.
http://www.lassp.cornell.edu/sethna/
A: As how it's titled, Complexity: A guided tour is a guided tour to complexity sciences. There is no formula in the book, but it does discuss many results and give you pointers. The author is a student of Douglas Hofstadter. She has a talk here
FYI: @Chris Aldrich also shares many helpful links in Are there any theories using thermodynamics/statistical mechanics or information theory principles to modelling in ecology?
