Introduction to the Theory of (Non-Symmetric) Dirichlet Forms

0 Introduction.- I Functional Analytic Background.- 1 Resolvents, semigroups, generators.- 2 Coercive bilinear forms.- 3 Closability.- 4 Contraction properties.- 5 Notes/References.- II Examples.- 1 Starting point: operator.- 2 Starting point: bilinear form - finite dimensional case.- 3 Starting point: bilinear form - infinite dimensional case.- 4 Starting point: semigroup of kernels.- 5 Starting point: resolvent of kernels.- 6 Notes/References.- III Analytic Potential Theory of Dirichlet Forms.- 1 Excessive functions and balayage.- 2 ?-exceptional sets and capacities.- 3 Quasi-continuity.- 4 Notes/References.- IV Markov Processes and Dirichlet Forms.- 1 Basics on Markov processes.- 2 Association of right processes and Dirichlet forms.- 3 Quasi-regularity and the construction of the process.- 4 Examples of quasi-regular Dirichlet forms.- 5 Necessity of quasi-regularity and some probabilistic potential theory.- 6 One-to-one correspondences.- 7 Notes/References.- V Characterizationof Particular Processes.- 1 Local property and diffusions.- 2 A new capacity and Hunt processes.- 3 Notes/References.- VI Regularization.- 1 Local compactification.- 2 Consequences - the transfer method.- 3 Notes/References.- A Some Complements.- 1 Adjoint operators.- 2 The Banach/Alaoglu and Banach/Saks theorems.- 3 Supplement on Ray resolvents and right processes.