The goal of this book is to present the most thorough treatment of normal forms that currently exists in book form. Presently there is a big gap between the elementary treatments in textbooks and the advanced research papers on normal forms. The targeted audience for this book is Ph.D. students and researchers in applied mathematics, theoretical physics, and advanced engineering. While it is self- contained and could in principle be read by anyone with a sufficient background in linear algebra and differential equations, it is assumed that most readers will have had some previous exposure to dynamical systems.