Weak KAM Theory

The weak KAM theory is currently one of the most active research topics in the domainof Hamiltonian dynamical systems. Based on the Mather theory, the French mathematicianFathi founded the weak KAM theory in the mid-1990s, which focuses on the research of thedynamics of convex Hamiltonian systems. In view of its important theoretical and practicalvalue, the weak KAM theory attracts more and more attention of domestic and foreign math-ematicians, and has been developing rapidly. In this thesis, we will give a brief introductionto the weak KAM theory. From the rudiments of the Mather theory to the classical results ofthe weak KAM theory, we try to clearly reveal its theoretical development path by dividingthe thesis into14chapters.