Recommendations on the foundations of statistical physics/thermodynamics

Hi all,

I'm following course on statistical physics for my theoretical physics master right now, and I would like to refresh my knowledge on the foundations of statistical physics and thermodynamics (since that is pretty much considered as known under the participants). I'm interested in literature that strives to be very rigorous, for I do have some knowledge of the basic concepts, but not so much (anymore) of their foundations/definitions/derivations. Do you have any recommendations for literature I can consult for this?

Examples of things I would like to have a more rigorous understanding of are, on the statistical physics side: the definition of the partition function and a derivation of it's relation to entropy, and on the thermodynamical side: the derivation of the entropy function and it's relation to the canoncial, micro-canonical, grand-canonical ensemble (and others). And on a more general note, what grounds there are for connecting both theories (like, why the statistical definition of the entropy should equal the thermodynamical one in the thermodynamic limit).

Thanks in advance!