| Preface | p. xi |
| Introduction | p. 1 |
| The leitmotiv | p. 1 |
| A few words about the history of entropy | p. 3 |
| Multiple meanings of entropy | p. 4 |
| Conventions | p. 18 |
| Entropy in ergodic theory | p. 21 |
| Shannon information and entropy | p. 23 |
| Information and entropy of probability vectors | p. 23 |
| Partitions and sigma-algebras | p. 30 |
| Information and static entropy of a Partition | p. 32 |
| Conditional static entropy | p. 33 |
| Conditional entropy via probabilistic tools* | p. 35 |
| Basic properties of static entropy | p. 36 |
| Metrics on the space of Partitions | p. 42 |
| Mutual information* | p. 46 |
| Non-Shannon inequalities* | p. 48 |
| Exercises | p. 51 |
| Dynamical entropy of a process | p. 53 |
| Subadditivity | p. 53 |
| Preliminaries on dynamical systems | p. 57 |
| Dynamical entropy of a process | p. 60 |
| Properties of dynamical entropy | p. 65 |
| Affinity of dynamical entropy | p. 68 |
| Conditional dynamical entropy via disintegration* | p. 69 |
| Summary of the properties of entropy | p. 72 |
| Combinatorial entropy | p. 73 |
| Exercises | p. 78 |
| Entropy theorems in processes | p. 80 |
| Independence and -independence | p. 80 |
| The Pinsker sigma-algebra in a process | p. 85 |
| The Shannon-McMillan-Breiman Theorem | p. 89 |
| The Ornstein-Weiss Return Times Theorem | p. 94 |
| Horizontal data compression | p. 97 |
| Exercises | p. 100 |
| Kolmogorov-Sinai Entropy | p. 102 |
| Entropy of a dynamical system | p. 102 |
| Generators | p. 105 |
| The natural extension | p. 111 |
| Joinings | p. 116 |
| Ornstein Theory* | p. 120 |
| Exercises | p. 130 |
| The Ergodic Law of Series* | p. 132 |
| History of the Law of Series | p. 132 |
| Attracting and repelling in signal processes | p. 135 |
| Decay of repelling in positive entropy | p. 139 |
| Typicality of attracting for long cylinders | p. 152 |
| Entropy in topological dynamics | p. 157 |
| Topological entropy | p. 159 |
| Three definitions of topological entropy | p. 159 |
| Properties of topological entropy | p. 165 |
| Topological conditional and tail entropies | p. 167 |
| Properties of topological conditional entropy | p. 171 |
| Topological joinings | p. 172 |
| The simplex of invariant measures | p. 175 |
| Topological fiber entropy | p. 179 |
| The major Variational Principles | p. 181 |
| Determinism in topological systems | p. 190 |
| Topological preimage entropy* | p. 197 |
| Exercises | p. 199 |
| Dynamics in dimension zero | p. 201 |
| Zero-dimensional dynamical systems | p. 201 |
| Topological entropy in dimension zero | p. 202 |
| The invariant measures in dimension zero | p. 203 |
| The Variational Principle in dimension zero | p. 205 |
| Tail entropy and asymptotic h-expansiveness in dimension zero | p. 206 |
| Principal zero-dimensional extensions | p. 212 |
| Exercises | p. 225 |
| The entropy structure | p. 227 |
| The type of convergence | p. 227 |
| U.s.d.a.-sequences on simplices | p. 244 |
| Entropy of a measure with respect to a topological resolution | p. 254 |
| Entropy structure | p. 263 |
| Exercises | p. 270 |
| Symbolic extensions | p. 272 |
| What are symbolic extensions? | p. 272 |
| The Symbolic Extension Entropy Theorem | p. 274 |
| Properties of symbolic extension entropy | p. 287 |
| Symbolic extensions of interval maps | p. 293 |
| Exercises | p. 301 |
| A touch of smooth dynamics* | p. 303 |
| Margulis-Ruelle Inequality and Pesin Entropy Formula | p. 303 |
| Tail entropy estimate | p. 307 |
| Symbolic extensions of smooth systems | p. 308 |
| Entropy theory for operators | p. 311 |
| Measure-theoretic entropy of stochastic operators | p. 313 |
| A few words on operator dynamics | p. 313 |
| The axiomatic measure-theoretic definition | p. 316 |
| An explicit measure-theoretic definition | p. 329 |
| Not so bad properties of the operator entropy | p. 332 |
| Exercises | p. 335 |
| Topological entropy of a Markov operator | p. 336 |
| Three definitions | p. 336 |
| Properties of the topological operator entropy | p. 339 |
| Half of the variational principle | p. 341 |
| Exercises | p. 343 |
| Open problems in operator entropy | p. 344 |
| Questions on doubly stochastic operators | p. 344 |
| Questions concerning Markov operators | p. 345 |
| Toolbox | p. 347 |
| Conditional S-M-B | p. 366 |
| List of symbols | p. 374 |
| References | p. 379 |
| Index | p. 386 |
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