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:
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.