An Overview of the Book -- Optimal Markovian Couplings -- New Variational Formulas for the First Eigenvalue -- Generalized Cheeger's Method -- Ten Explicit Criteria in Dimension One -- Poincare-Type Inequalities in Dimension One -- Functional Inequalities -- A Diagram of Nine Types of Ergodicity -- Reaction-Diffusion Processes -- Stochastic Models of Economic Optimization