Dynamical Systems and Chaos is a new scientific field that has developed over the last 20 years and has already significantly impacted research in almost all physical sciences, radically changing the way we approach many phenomena of daily life that we used to call "complex," "random," or "unpredictable."

The central axis of this new scientific direction is Mathematics, specifically the study of systems of nonlinear equations that describe the dynamics of a chaotic phenomenon: From turbulent flow of a fluid and non-harmonic oscillations of structures, to cardiac arrhythmia, seismic vibrations, and fluctuations in the stock market.

This book attempts a first introduction to the basic principles, methods, and applications of Dynamical Systems and Chaos, from a pedagogical perspective. There are many examples, exercises, and references to experimental results that help the reader better understand the new and somewhat unusual concepts of nonlinear systems and chaotic dynamics.

The first volume contains a review of the major discoveries in nonlinear chaotic dynamics and aims to engage the reader and spark interest in the study of this new field. The mathematical knowledge required is taught in the first two years of Physical-Mathematical and Polytechnic Schools of Greek Higher Education Institutions.