Dirichlet forms : lectures given at the 1st session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Varenna, Italy, June 8-19, 1992

Gaussian upper bounds on fundamental solutions of parabolic equations the method of nash.- Two topics related to Dirichlet forms: quasi everywhere convergences and additive functionals.- Logarithmic Sobolev inequalities and contractivity properties of semigroups.- Potential theory of non-divergence form elliptic equations.- General theory of Dirichlet forms and applications.- Logarithmic Sobolev inequalities for gibbs states.