CONTENTS Introduction § 1. The multiplicative ergodic theorem § 2. Quasi-projective transformations § 3. Contraction property of a semigroup § 4. Invariant measure and lemmas on convergence § 5. Fundamental theorem on Lyapunov indices § 6. Generalization of the fundamental theorem and the multiplicity of indices. Kotani's result § 7. Example: Lyapunov indices of a difference matrix Schrödinger equation Appendix References