Operator Theoretic Aspects of Ergodic Theory Stunning recent results by Host Kra Green Tao and others highlight the timeliness of this systematic introduction to classical ergodic theory using the tools of operator theory. Assuming no prior exposure to ergodic theory this book provides a modern foundation for introductory courses on ergodic theory especially for students or researchers with an interest in functional analysis. While basic analytic notions and results are reviewed in several appendices more advanced operator theoretic topics are developed in detail even beyond their immediate connection with ergodic theory. As a consequence the book is also suitable for advanced or special topic courses on functional analysis with applications to ergodic theory. Topics include: •an intuitive introduction to ergodic theory •an introduction to the basic notions constructions and standard examples of topological dynamical systems •Koopman operators Banach lattices lattice and algebra homomorphisms and the Gelfand Naimark theorem •measure preserving dynamical systems •von Neumann’s Mean Ergodic Theorem and Birkhoff’s Pointwise Ergodic Theorem •strongly and weakly mixing systems •an examination of notions of isomorphism for measure preserving systems •Markov operators and the related concept of a factor of a measure preserving system •compact groups and semigroups and a powerful tool in their study the Jacobs de Leeuw Glicksberg decomposition •an introduction to the spectral theory of dynamical systems the theorems of Furstenberg and Weiss on multiple recurrence and applications of dynamical systems to combinatorics (theorems of van der Waerden Gallai and Hindman Furstenberg’s Correspondence Principle theorems of Roth and Furstenberg Sárközy) Beyond its use in the classroom Operator Theoretic Aspects of Ergodic Theory can serve as a valuable foundation for doing research at the intersection of ergodic theory and operator theory What is Ergodic Theory Topological Dynamical Systems Minimality and Recurrence The C* algebra C(K) and the Koopman Operator Measure Preserving Systems Recurrence and Ergodicity The Banach Lattice Lp and the Koopman Operator The Mean Ergodic Theorem Mixing Dynamical Systems Mean Ergodic Operators on C(K) The Pointwise Ergodic Theorem Isomorphisms and Topological Models Markov Operators Compact Semigroups and Groups Topological Dynamics Revisited The Jacobs de Leeuw Glicksberg Decomposition Dynamical Systems with Discrete Spectrum A Glimpse at Arithmetic Progressions Joinings The Host Kra Tao Theorem More Ergodic Theorems Appendix A: Topology Appendix B: Measure and Integration Theory Appendix C: Functional Analysis Appendix D: The Riesz Representation Theorem Appendix E: Theorems of Eberlein Grothendieck and Ellis