Part. 1. Group Theory: Introduction to groups -- Subgroups -- Quotient groups and homomorphisms -- Group actions -- Direct and semidirect products and abelian groups -- Further topics in group theory -- Part 2. Ring theory: Introduction to rings -- Euclidean domains, principal ideal domains and unique factorization domains -- Polynomial rings -- Part 3. Modules and vector spaces: Introduction to module theory -- Vector spaces -- Modules over principal ideal domains -- Part. 4. Field theory and Galois theory: Field theory -- Galois theory -- Part 5. An introduction to commutative rings, algebraic geometry, and homological algebra: Commutative rings and algebraic geometry -- Artinian rings, discrete valuation rings, and Dedekind domains -- Introduction to homological algebra and group cohomology -- Part 6. Introduction to the representation theory of finite groups: Representation theory and character theory -- Examples and applications of character theory