This book is about probabilistic aspects of discrete dynamical systems andtheir computer simulations. Basic measure theory is used as a theoretical toolto describe probabilistic phenomena. All of the simulations are done using themathematical software Maple, which enables us to translate theoretical ideasinto computer programs word by word avoiding any other technical details.The level of familiarity with computer programming is kept minimal. Thuseven theoretical mathematicians can appreciate the experimental nature ofone of the fascinating areas in mathematics.A new philosophy is introduced even for those who are already familiarwith numerical simulations of dynamical systems. Most computer experimentsin this book employ many significant digits depending on the entropy of thegiven transformation so that they can still produce meaningful results aftermany iterations. This is why we can do experiments that have not been triedelsewhere before. It is the main point of the book. Readers should regard theMaple programs as important as the theoretical explanations of mathematicalfacts. The book is designed in such a way that theoretical and experimentalparts complement each other.A dynamical system is a set of points together with a transformationrule that describes the movement of points. Sometimes the points lose thegeometrical implication and they are just elements in an abstract set that hascertain structures depending on the type of the problem under consideration.The theory of dynamical systems studies the long term statistical behavior ofthe points under the transformation rules. When the given set of points hasa probabilistic structure, the theory of dynamical systems is called ergodictheory. The aim of the book is to study computational aspects of ergodictheory including data compression.Many mathematical concepts introduced in the book are illustrated bycomputer simulations. That gives a different flavor to ergodic theory, andmay attract a new generation of students who like to play with computers.Some theorems look different, at least to beginners, when the abstract factsare explained in terms of computer simulations. Many computer experiments

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