This self-contained 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. The reader needs a basic knowledge of real analysis,...