Preface.- 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.- Poincar‚-type Inequalities in Dimension One.- Functional Inequalities.- A Diagram of Nine Types of Ergodicity.- Reaction-Diffusion Processes.- Stochastic Models of Economic Optimization.- Appendix A: Some Elementary Lemmas.- Appendix B: Examples of Ising Model on Two-Four Sites.- References.- Author Index.- Subject Index.