This book is designed to introduce the reader to the theory of Lie algebras. Lie algebras are used in many different areas. Besides being useful in many parts of mathematics and physics, the theory of Lie algebras is inherently attractive. This book aims to give a rigorous treatment of the fundamentals of Lie algebra with numerous examples to show the concepts. I have tried to make all arguments as simple and direct as I could, without entering into too many possible ramifications. I hope this book will also enable the reader to enter into the more advanced phases of the theory.