  These are introductory lecture notes on Mather's theory for Tonelli
Lagrangian and Hamiltonian systems. They are based on a series of lectures
given by the author at Universit\`a degli Studi di Napoli "Federico II" (April
2009), at University of Cambridge (academic year 2009-2010) and at Universitat
Polit\`ecnica de Catalunya (June 2010).
