1. Introduction

Dynamical systems theory and probability theory are basic tools of science. They are mathematical theories. They are used to describe, understand, model, and predict systems in quantitative sciences such as physics, biology, and economics. The time evolution of many of these systems is governed by dynamical laws that can be cast into a common mathematical form that makes them a dynamical system. Dynamical systems theory studies the properties of these systems independent of the context in which they arise. Science also has to deal with uncertainty. We do not know exactly that an event will occur under certain circumstances or as the outcome of a certain experiment. Mathematicians have developed the concept of probability to quantify uncertainty. Uncertainty may be intrinsic, quantum mechanics being the prime example; or it may be epistemic, due to our lack of complete knowledge or control. Though probability theory grew out of the analysis of games of chances it is also an axiomatic theory independent of any specific context. Part I and Part II of this book review dynamical systems theory and probability theory.