Group theory is an important subject that has come a long way in recent years. Introduction to Group Theory presents the fundamentals of both finite and infinite group theory, with a focus on finite groups. It provides students with the ability to prove the Thomas normal p-complement theorem and to classify simple finite groups. A large portion of the text is devoted to general linear groups. Additional topics covered include the construction of BN pairs, Coexeter groups, Hall-Higham theory, and Bender results. The text also offers an in-depth exploration of the complex relationship between groups, coding, and cryptography.