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Chapter 3 treats linear transformations, their algebra, their representation by matrices, as well as to get access to your one-sheeter, Centralizers and Normalizers, Stabilizers and Kernels, Subgroups Generated by Subsets of a Group, Composition Series and the Holder Program, Group Actions and Permutation Representations, Groups Acting on Themselves by Left Multiplication - Cayley's Theorem, Group's Acting on Themselves by Conjugation -The Class Equation, The Fundamental Theorem of Finitely Generated Abelian Groups, p-Groups, Nilpotent Groups, and Solvable Groups, Examples: Polynomial Rings, Matrix Rings, and Group Rings, Polynomial Rings That are Unique Factorization Domains, Polynomials in Several Variables Over a Field Grobner Bases, Quotient Modules and Module Homomorphisms, Generation of Modules, Direct Sums, and Free Modules, Exact Sequences - Projective, Injective, and Flat Modules, Tensor Algebras, Symmetric and Exterior Algebras, Classical Straightedge and Compass Constructions, Composite Extensions and Simple Extensions, Cyclotomic Extensions and Abelian Extensions over Q, Solvable and Radical Extensions: Insolvability of the Quintic, Transcendental Extensions, Inseparable Extensions, Infinite Galois Groups, Noetherian Rings and Affine Algebraic Sets, Integral Extensions and Hilbert's Nullstellensatz, Introduction to Homological Algebra - Ext and Tor, Group Extensions, Factor Sets and H2 (G,A), Linear Actions and Modules over Group Rings, Wedderburn's Theorem and Some Consequences, Character Theory and the Orthogonality Relations, Introduction to the Theory of Induced Characters. 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