Algebraic Equations.- Three Muslimic Authors.- Algebra in Italy.- From Viète to Descartes.- The Predecessors of Galois.- Carl Friedrich Gauss.- Evariste Galois.- Camille Jordan.- Groups.- Early Group Theory.- Lie Groups and Lie Algebras.- Algebras.- The Discovery of Algebras.- The Structure of Algebras.- Group Characters.- Representations of Finite Groups and Algebras.- Representations of Lie Groups and Lie Algebras.