This book is a systematic introduction to smooth ergodic theory. The topics discussed include the general (abstract) theory of Lyapunov exponents and its applications to the stability theory of differential equations, stable manifold theory, absolute continuity, and the ergodic theory of dynamical systems with nonzero Lyapunov exponents (including geodesic flows). The authors consider several nontrivial examples of dynamical systems with nonzero Lyapunov exponents to illustrate some basic methods and ideas of the theory. This book is selfcontained. The reader needs a basic knowledge of real analysis, measure theory, differential equations, and topology. The authors present basic concepts of smooth ergodic theory and provide complete proofs of the main results. They also state some more advanced results to give readers a broader view of smooth ergodic theory. This volume may be used by those nonexperts who wish to become familiar with the field. Readership Graduate students and research mathematicians interested in dynamical systems and ergodic theory. Reviews "Even though there are a very great number of publications on this subject, the book from Barreira and Pesin in the first comprehensive textbook. It is highly worth recommending both to advanced and interested students and to scientists working on dynamical systems ... The book is selfcontained and gets by to a great extent without additional references. It has a clear and well thoughtout structure and forgoes any unnecessary complexity of notation."  translated from Jahresbericht der Deutschen MathematikerVereinigung "Compact and useful selfcontained book ... a rich array of examples ... this is a handy and lucid book on a tricky subject."  Mathematical Reviews Table of Contents  Introduction
 Lyapunov stability theory of differential equations
 Elements of nonuniform hyperbolic theory
 Examples of nonuniformly hyperbolic systems
 Local manifold theory
 Ergodic properties of smooth hyperbolc measures
 Bibliography
 Index
