This book, the fourth book in the four-volume series in algebra, discusses Lie algebra and representation theory in detail. It covers topics such as semisimple Lie algebras, root systems, representation theory of Lie algebra, Chevalley groups and representation theory of Chevalley groups. Numerous motivating illustrations have been presented along with exercises, enabling readers to acquire a good understanding of topics which they can then use to find the exact or most realistic solutions to their problems.