Preface to the first and second edition -- Preface to the second edition -- Contents -- Notation -- I Dirichlet Forms -- 1 Basic theory of Dirichlet forms -- 1.1 Basic notions -- 1.2 Examples -- 1.3 Closed forms and semigroups -- 1.4 Dirichlet forms and Markovian semigroups -- 1.5 Transience of Dirichlet spaces and extended Dirichlet spaces -- 1.6 Global properties of Markovian semigroups -- 2 Potential theory for Dirichlet forms -- 2.1 Capacity and quasi continuity -- 2.2 Measures of finite energy integrals -- 2.3 Reduced functions and spectral synthesis -- 2.4 Capacities and Sobolev type inequalities -- 3 The scope of Dirichlet forms -- 3.1 Closability and the smallest closed extensions -- 3.2 Formulae of Beurling-Deny and LeJan -- 3.3 Maximum Markovian extensions -- II Symmetric Markov processes -- 4 Analysis by symmetric Hunt processes -- 4.1 Smallness of sets and symmetry -- 4.2 Identification of potential theoretic notions -- 4.3 Orthogonal projections and hitting distributions -- 4.4 Parts of forms and processes -- 4.5 Continuity, killing, and jumps of sample paths -- 4.6 Quasi notions, fine notions and global properties -- 4.7 Irreducible recurrence and ergodicity -- 4.8 Recurrence and Poincaré type inequalities -- 5 Stochastic analysis by additive functionals -- 5.1 Positive continuous additive functionals and smooth measures -- 5.2 Decomposition of additive functionals of finite energy -- 5.3 Martingale additive functionals and Beurling-Deny formulae -- 5.4 Continuous additive functionals of zero energy -- 5.5 Extensions to additive functionals locally of finite energy -- 5.6 Martingale additive functionals of finite energy and stochastic integrals -- 5.7 Forward and backward martingale additive functionals -- 6 Transformations of forms and processes.

6.1 Perturbed Dirichlet forms and killing by additive functionals -- 6.2 Traces of Dirichlet forms and time changes by additive functionals -- 6.2.1 Transient case -- 6.2.2 General case -- 6.3 Transformations by supermartingale multiplicative functionals -- 6.4 Donsker-Varadhan type large deviation principle -- 7 Construction of symmetric Markov processes -- 7.1 Construction of a Markovian transition function -- 7.2 Construction of a symmetric Hunt process -- Appendix -- A.1 Choquet capacities -- A.2 An introduction to Hunt processes -- A.3 A summary on martingale additive functionals -- A.4 Regular representations of Dirichlet spaces -- A.5 Solutions to Exercises -- Notes -- Bibliography -- Index.