This revised edition of Notes on Lie Algebras covers structuring, classification, and representations of semisimple Lie algebras, a classical field that has become increasingly important to mathematicians and physicists. The text's purpose is to introduce the student to the basic facts and their derivations using a direct approach in today's style of thinking and language. The main prerequisite for a clear understanding of the book is Linear Algebra, of a reasonably sophisticated nature. For this revised edition, errors have been eliminated, a number of proofs have been rewritten with more clarity, and some new material has been added.