Statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the macroscopic behavior of nature from the behavior of such ensembles. Thermodynamics is the branch of physics that deals with the relationships between heat and other forms of energy. In particular, it describes how thermal energy is converted to and from other forms of energy and how it affects matter, these topics are important to know: The first, second and third laws of thermodynamics, The Carnot cycles. Entropy. Heat engines, Canonical Ensembles, The Boltzmann distribution, Planck's distribution, Fermi-Dirac statistics, Bose-Einstein statistics, Phase transitions. Thermodynamical models, Planck’s radiation law (as a prelude to Quantum Mechanics). 

There are many textbooks that cover the statistical mechanics topic we need as a physicist, such as: Statistical Mechanics by Kerson Huang and Statistical Mechanics by R. Pathria, P. Beale. Also you can see Prof. David Tong free lectures of Kinetic Theory and Statistical Physics.