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This volume offers an account of the present state of the art in pseudoperiodic topology---a young branch of mathematics, born at the boundary between the ergodic theory of dynamical systems, topology, and number theory. Related topics include the theory of algorithms, convex integer polyhedra, Morse inequalities, real algebraic geometry, statistical physics, and algebraic number theory. The book contains many new results. Most of the articles contain brief surveys on the topics, making the volume accessible to a broad audience. From the Preface by V.I. Arnold: "The authors ... have done much to show how modern mathematics begets, from this sea of pathological counterexamples, remarkable general and universal laws, whose discovery would be unthinkable and whose formulation would be impossible in the naive set-theoretical setting." Machine Generated Contents Note: Preface -- On The Topology Of Quasiperiodic Functions -- S.m. Gusein-zade -- Statistics Of Klein Polyhedra And Multidimensional Continued Fractions -- M.l. Kontsevich And Yu. M. Suhov -- C'-generic Properties Of Boundary Operators In The Novikov Complex -- A. Pajitnov -- Pseudoperiodic Mappings -- D.a. Panov -- How Do The Leaves Of A Closed 1-form Wind Around A Surface? -- Anton Zorich. Ed. By Vladimir Arnold, Maxim Kontsevich, Anton Zorich. Includes Bibliographical References. Machine generated contents note: Preface On the Topology of Quasiperiodic Functions S. M. GUSEIN-ZADE Statistics of Klein Polyhedra and Multidimensional Continued Fractions M. L. KONTSEVICH AND YU. M. SUHOV C'-Generic Properties of Boundary Operators in the Novikov Complex A. PAJITNOV Pseudoperiodic Mappings D. A. PANOV How Do the Leaves of a Closed 1-form Wind Around a Surface? ANTON ZORICH. Offers an account of the present state of the art in pseudoperiodic topology - a young branch of mathematics, born at the boundary between the ergodic theory of dynamical systems, topology, and number theory. This book provides topics that include the theory of algorithms, convex integer polyhedra, Morse inequalities, and real algebraic geometry.