This book describes the manifestations of chaos in atoms and molecules. About ten years ago, atomic physics received a rejuvenating jolt from chaos theory with far-reaching implications. The study of chaos is today one of the most active and prolific areas in atomic physics. This is the first attempt to provide a coherent introduction to this fascinating area. In line with its scope, the book is divided into two parts. The first part (chapters 1-5) deals with the theory and principles of classical chaos. The ideas developed here are then applied to actual atomic and molecular physics systems in the second part of the book (chapters 6-10) covering microwave driven surface state electrons, the hydrogen atom in a strong microwave field, the kicked hydrogen atom, chaotic scattering with CsI molecules and the helium atom. The book contains many diagrams and a detailed references list.