What is Algebra? -- Fields -- Commutative Rings -- Homomorphisms and Ideals -- Modules -- Algebraic Aspects of Dimension -- The Algebraic View of Infinitesimal Notions -- Noncommutative Rings -- Modules over Noncommutative Rings -- Semisimple Modules and Rings -- Division Algebras of Finite Rank -- The Notion of a Group -- Examples of Groups: Finite Groups -- Examples of Groups: Infinite Discre…