Reference request for Gibbs measure Understanding the Gibbs measure seems to be essential to fulling understanding statistical mechanics. However, I don't know of any mathematically rigorous textbooks/lecture notes that talk about such subject. What are some good references that go into detail in the math and also provide examples of application in physics?

The basic reference for Gibbs measures and phase transition is Georgii's book. It covers a lot of topics on the subject. Other good (book) references are Velenik and Friedli's book and Sinai's book. These, however, are not totally dedicated to Gibbs measures, also covering various statistical mechanics topics.

There are other lecture notes that are very helpful and well-written. For instance I can cite Arnaud's text, Anton Bovier's text (which has a part II also avaiable) and R. Fernández's text.