This textbook is ideal for advanced undergraduate or first-graduate students who want to learn the fundamentals of Lie groups. It covers the principles behind the theory and includes numerous applications and examples. The author's approach is unique - where some texts develop Lie group theory from matrix groups, differential geometry plays a more prominent role in this book. Most students will not have a background in differential geometry and for that reason, the authors have included an introduction to the topic that begins at the ground level. Each section engages the reader in an in-depth instruction on some of the most important, yet basic principles of Lie theory. In addition to these core topics, the authors include more recent research.

Students gain the ability to work through problems following the basic principles of Lie theory, understand references to Lie theoretic concepts, and easily move on to more advanced topics.