0 Preliminaries. - 0. 1 Introduction. - 0. 2 Measure Spaces. - 0. 3 Integration. - 0. 4 Absolutely Continuous Measures and Conditional Expectations. - 0. 5 Function Spaces. - 0. 6 Haar Measure. - 0. 7 Character Theory. - 0. 8 Endomorphisms of Tori. - 0. 9 PerronFrobenius Theory. - 0. 10 Topology. - 1 Measure-Preserving Transformations. - 1. 1 Definition and Examples. - 1. 2 Problems in Ergodic Theory. - 1. 3 Associated Isometries. - 1. 4 Recurrence. - 1. 5 Ergodicity. - 1. 6 The Ergodic Theorem. - 1. 7 Mixing. - 2 Isomorphism Conjugacy and Spectral Isomorphism. - 2. 1 Point Maps and Set Maps. - 2. 2 Isomorphism of Measure-Preserving Transformations. - 2. 3 Conjugacy of Measure-Preserving Transformations. - 2. 4 The Isomorphism Problem. - 2. 5 Spectral Isomorphism. - 2. 6 Spectral Invariants. - 3 Measure-Preserving Transformations with Discrete Spectrum. - 3. 1 Eigenvalues and Eigenfunctions. - 3. 2 Discrete Spectrum. - 3. 3 Group Rotations. - 4 Entropy. - 4. 1 Partitions and Subalgebras. - 4. 2 Entropy of a Partition. - 4. 3 Conditional Entropy. - 4. 4 Entropy of a Measure-Preserving Transformation. - 4. 5 Properties of h (T A) and h (T). - 4. 6 Some Methods for Calculating h (T). - 4. 7 Examples. - 4. 8 How Good an Invariant is Entropy?. - 4. 9 Bernoulli Automorphisms and Kolmogorov Automorphisms. - 4. 10 The Pinsker ?-Algebra of a Measure-Preserving Transformation. - 4. 11 Sequence Entropy. - 4. 12 Non-invertible Transformations. - 4. 13 Comments. - 5 Topological Dynamics. - 5. 1 Examples. - 5. 2 Minimality. - 5. 3 The Non-wandering Set. - 5. 4 Topological Transitivity. - 5. 5 Topological Conjugacy and Discrete Spectrum. - 5. 6 Expansive Homeomorphisms. - 6 Invariant Measures for Continuous Transformations. - 6. 1 Measures on Metric Spaces. - 6. 2 Invariant Measures for Continuous Transformations. - 6. 3 Interpretation of Ergodicity and Mixing. - 6. 4 Relation of Invariant Measures to Non-wandering Sets Periodic Points and Topological Transitivity. - 6. 5 Unique Ergodicity. - 6. 6 Examples. - 7 Topological Entropy. -7. 1 Definition Using Open Covers. - 7. 2 Bowen's Definition. - 7. 3 Calculation of Topological Entropy. - 8 Relationship Between Topological Entropy and Measure-Theoretic Entropy. - 8. 1 The Entropy Map. - 8. 2 The Variational Principle. - 8. 3 Measures with Maximal Entropy. - 8. 4 Entropy of Affine Transformations. - 8. 5 The Distribution of Periodic Points. - 8. 6 Definition of Measure-Theoretic Entropy Using the Metrics dn. - 9 Topological Pressure and Its Relationship with Invariant Measures. - 9. 1 Topological Pressure. - 9. 2 Properties of Pressure. - 9. 3 The Variational Principle. - 9. 4 Pressure Determines M(X T). - 9. 5 Equilibrium States. - 10 Applications and Other Topics. - 10. 1 The Qualitative Behaviour of Diffeomorphisms. - 10. 2 The Subadditive Ergodic Theorem and the Multiplicative Ergodic Theorem. - 10. 3 Quasi-invariant Measures. - 10. 4 Other Types of Isomorphism. - 10. 5 Transformations of Intervals. - 10. 6 Further Reading. - References. Language: English