Kolmogorov Equations for Stochastic PDEs The subject of this book is stochastic partial differential equations in particular reaction diffusion equations Burgers and Navier Stokes equations and the corresponding Kolmogorov equations. For each case the transition semigroup is considered and irreducibility the strong Feller property and invariant measures are investigated. Moreover it is proved that the exponential functions provide a core for the infinitesimal generator. As a consequence it is possible to study Sobolev spaces with respect to invariant measures and to prove a basic formula of integration by parts (the so called carré du champs identity . Several results were proved by the author and his collaborators and appear in book form for the first time. Presenting the basic elements of the theory in a simple and compact way the book covers a one year course directed to graduate students in mathematics or physics. The only prerequisites are basic probability (including finite dimensional stochastic differential equations) basic functional analysis and some elements of the theory of partial differential equations