There are apparently only a few books on rigorous results in statistical mechanics. David Ruelle's books are apparently standard, though I found them difficult to digest when I picked them up. One which I found more accessible is "Introduction to Mathematical Statistical Physics" by Minlos.

A personal note is that I found statistical mechanics very unintuitive and difficult to learn at first. I felt that the formalism didn't come together for me until I was familiar with a multitude of physical systems.

A more advanced book which I really love for giving physical intuition is Cardy's book on the renormalization group (though this thin book is very light on rigor!)