¿In this book the author presents a self-contained account of Harnack inequalities and applications for the semigroup of solutions to stochastic partial and delayed differential equations. Since the semigroup refers to Fokker-Planck equations on infinite-dimensional spaces, the Harnack inequalities the author investigates are dimension-free. This is an essentially different point from the above mentioned classical Harnack inequalities. Moreover, the main tool in the study is a new coupling method (called coupling by change of measures) rather than the usual maximum principle in the current literature.

A General Theory on Dimension-Free Harnack Inequalities.- Non-Linear Monotone Stochastic Partial Differential Equations.- Semi-linear Stochastic Partial Differential Equations .- Stochastic Functional (Partial) Differential Equations.- Non-Linear Monotone Stochastic Partial Differential Equations.- Semi-linear Stochastic Partial Differential Equations.- Stochastic Functional (Partial) Differential Equations.