Recommendations for statistical mechanics book I learned thermodynamics and the basics of statistical mechanics but I'd like to sit through a good advanced book/books. Mainly I just want it to be thorough and to include all the math. And of course, it's always good to give as much intuition about the material.
Some things I'd be happy if it includes (but again, it mostly just needs to be a clear book even if it doesn't contain these) are:


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*As much justifications for the postulates if possible, I'm very interested in reading more about how Liouville's theorem connects to the postulates.

*Have examples of calculating partition functions, hopefully not just the partition function for the ideal gas.
 A: I recommend books by Kardar
"Statistical Physics of Particles"
"Statistical Physics of Fields"
The mordern approach to this subject is helpful for your future study.
Also there are solutions to all of the problem, which you can find from the internet.
A: As an undergrad, we used "Thermal Physics" by Kittel and Kroemer:
http://www.amazon.com/Thermal-Physics-Edition-Charles-Kittel/dp/0716710889
A: If anyone is interested in seeing how this is done from a chemist's perspective I can heartily recommend Statistical Mechanics: Theory and Molecular Simulation by Mark Tuckerman.  Sadly, it isn't on line but can be ordered from Amazon or the like.
A: It has to be " Statistical Mechanics and Thermodynamics " by Claude Garrod". You can use the text by Macquarie as a supplement. For renormalization group and advanced concepts, use " Statistical Physics of Fields" by Kardar.
A: Greiner's Thermodynamics and Statistical Mechanics is pretty good from a few short readings I did. Also, it has better reviews from almost all of the other popular textbooks on the subject in goodreads.com
A: EDIT: My answer assumes that you're looking for a book at the introductory graduate level.
I found Pathria's "Statistical Mechanics" (2nd ed) very helpful during my first-year graduate statistical mechanics course.  Pathria's treatment of the subject is mathematically careful and detailed, at least by physics standards; I found his discussion of Liouville's theorem (part 1 of your question) satisfactory.  Unfortunately, like many formal treatments, Pathria discusses few interesting applications.
"Statistical Physics of Particles" by Kardar appears to be supplanting Pathria as the favored introductory graduate text; it was used at Boston University and at Caltech during my time there.  Kardar is very terse and would probably have to be supplemented by another book, but the problems he offers are interesting (if hard).  In fact, about a third of the text consists of detailed solutions to the problems.
I have heard good things about Reichl's book, already mentioned in another answer.  I used it briefly as a reference: the coverage of kinetic theory is more complete than in other sources.  It is more accessible than Pathria, not to mention Kardar.
A: I recommend the book A Modern Course in Statistical Physics by Reichl.
It starts with phenomenological thermodynamics, covers both equilibrium and nonequilibrium statistical mechanics, and discusses a wide range of applications,
not only ideal and real gases. Its level of rigor is that of typical books on theoretical physics.
You may also be interested in my online book https://arxiv.org/abs/0810.1019
the part on statistical mechanics is nearly independent of the remainder.
A: It may sound old but  0."An introduction to statistical physics- by A.J. Pointon" is a very handy book to absorb the concept of calculation over phase space from the very beginning. The book is suitable for a one semester course, designed for last year undergraduate and beginning graduate students. The exposition of this book is exceptionally clear. It hardly skips any mathematics under the hood. 
For more advanced treatment of the subject there are plenty of other good books. The list is not exhaustive at all..


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*Statistical Mechanics, 2nd Edition by Kerson Huang

*A Modern Course in Statistical Physics 4th ( & 2nd) Edition by Linda E. Reichl 

*Statistical Physics: Volume 5 3rd Edition by L.D. Landau, E. M. Lifshitz

*Statistical Physics of Particles 1st Edition by Mehran Kardar 

*Statistical Mechanics 3rd Edition by R K Pathria, Paul D. Beale


One may also get interest into the book - 
6. Introduction to Modern Statistical Mechanics 1st Edition by David Chandler.
The approach of this book to the subject is very different than the above mentioned books. 
