One of the few books on Ordinary Differential Equations (ODEs), this book contains both qualitative theory, allowing students to analyze the solutions without obtaining formulas, and methods and techniques for obtaining formulas. It features friendly explanations of theorems on top of their formal proofs, expressed in examples, questions, figures, exercises, fun models related to various aspects of life, and even Math Theater explaining, using ODEs, the advantage of optimization by feedback versus a rigid plan. Exercises, both simple and more advanced levels, can be found within.This will allow students to deal with ODEs with a full understanding of what they are doing rather than manipulating with symbols, and even to extend themselves some theorems and techniques. The book is designed for students, teachers, and researchers. It can be used straightforwardly for a one-semester course on ODEs; alternatively, teachers might find it worthwhile to include some of the chapters in their course.