A very good book along the lines you seem to want is Gallavotti's *Statistical Mechanics - A Short Treatise*, which can be downloaded from [here][1]. He covers many of the classical topics, with a detailed discussions of foundational issues, the role of ergodicity/mixing, etc.

From a very different point of view, with a colleague, we are writing a mathematically rigorous introductory book to the equilibrium statistical mechanics of lattice systems. We hope to finish it for Summer 2016, but you can already download drafts of several chapters [here][2]. We are trying hard to make the book as readable and student-friendly as possible.


  [1]: https://ergodic.ugr.es/FisicaEstadistica/bibliografia/G%20Gallavotti%20SM%20%28359%29.pdf
  [2]: http://www.unige.ch/math/folks/velenik/smbook/