Copies of the classnotes are on the internet in PDF format as given below. The "Proofs of Theorems" files were prepared in Beamer. The "Printout of Proofs" are printable PDF files of the Beamer slides without the pauses.

Videos for these sections are online at the Online Modern Algebra: Groups webpage.

0. Introduction: Prerequisites and Preliminaries.

• Sections 0.1-0.6. Logic, Sets and Classes, Functions, Relations and Partitions, Products, Integers. Sections 0.1 to 0.6 notes
• Supplement. Proofs of Theorems in Sections 0.1-0.6. Beamer file of Sections 0.1 to 0.6 proofs
• Supplement. Printout of the Proofs of Theorems in Sections 0.1-0.6. Print file of Sections 0.1 to 0.6 proofs
• Section 0.7. The Axiom of Choice, Order, and Zorn's Lemma. Section 0.7 notes (Contains results implied by the Axiom of Choice.)
• Section 0.8. Cardinal Numbers. Section 0.8 notes (Contains a statement of the ZFC Axioms of set theory.)

I. Groups. Chapter I Introduction notes

• Section I.1. Semigroups, Monoids, and Groups. Section I.1 notes
• Supplement. Proofs of Theorems in Section I.1. Beamer file of Section I.1 proofs
• Supplement. Printout of the Proofs of Theorems in Section I.1. Print file of Section I.1 proofs
• Section I.2. Homomorphisms and Subgroups. Section I.2 notes
• Supplement. Proofs of Theorems in Section I.2. Beamer file of Section I.2 proofs
• Supplement. Printout of the Proofs of Theorems in Section I.2. Print file of Section I.2 proofs.
• Section I.3. Cyclic Groups. Section I.3 notes
• Supplement. Proofs of Theorems in Section I.3. Beamer file of Section I.3 proofs
• Supplement. Printout of the Proofs of Theorems in Section I.3. Print file of Section I.3 proofs
• Section I.4. Cosets and Counting. Section I.4 notes
• Supplement. Proofs of Theorems in Section I.4. Beamer file of Section I.4 proofs
• Supplement. Printout of the Proofs of Theorems in Section I.4. Print file of Section I.4 proofs
• Section I.5. Normality, Quotient Groups, and Homomorphisms. Section I.5 notes
• Supplement. Proofs of Theorems in Section I.5. Beamer file of Section I.5 proofs
• Supplement. Printout of the Proofs of Theorems in Section I.5. Print file of Section I.5 proofs
• Section I.6. Symmetric, Alternating, and Dihedral Groups. Section I.6 notes (Contains a proof that a permutation cannot be both even and odd.)
• Supplement. Proofs of Theorems in Section I.6. Beamer file of Section I.6 proofs
• Supplement. Printout of the Proofs of Theorems in Section I.6. Print file of Section I.6 proofs
• Section I.7. Categories: Products, Coproducts, and Free Objects. Section I.7 notes
• Supplement. Proofs of Theorems in Section I.7. Beamer file of Section I.7 proofs
• Supplement. Printout of the Proofs of Theorems in Section I.7. Print file of Section I.7 proofs
• Section I.8. Direct Products and Direct Sums. Section I.8 notes
• Supplement. Proofs of Theorems in Section I.8. Beamer file of Section I.8 proofs
• Supplement. Printout of the Proofs of Theorems in Section I.8. Print file of Section I.8 proofs
• Section I.9. Free Groups, Free Products, Generators & Relations. Section I.9 notes
• Supplement. Proofs of Theorems in Section I.9. Beamer file of Section I.9 proofs
• Supplement. Printout of the Proofs of Theorems in Section I.9. Print file of Section I.9 proofs
• Study Guide for Chapter I

II. The Structure of Groups.

• Section II.1. Free Abelian Groups. Section II.1 notes
• Supplement. Proofs of Theorems in Section II.1. Beamer file of Section II.1 proofs
• Supplement. Printout of the Proofs of Theorems in Section II.1. Print file of Section II.1 proofs
• Section II.2. Finitely Generated Abelian Groups. Section II.2 notes
• Supplement. Proofs of Theorems in Section II.2. Beamer file of Section II.2 proofs
• Supplement. Printout of the Proofs of Theorems in Section II.2. Print file of Section II.2 proofs
• Section II.3. The Krull-Schmidt Theorem. Section II.3 notes
• Supplement. Proofs of Theorems in Section II.3. Beamer file of Section II.3 proofs
• Supplement. Printout of the Proofs of Theorems in Section II.3. Print file of Section II.3 proofs
• Section II.4. The Action of a Group on a Set. Section II.4 notes
• Supplement. Proofs of Theorems in Section II.4. Beamer file of Section II.4 proofs
• Supplement. Printout of the Proofs of Theorems in Section II.4. Print file of Section II.4 proofs
• Section II.5. The Sylow Theorems. Section II.5 notes
• Supplement. Proofs of Theorems in Section II.5. Beamer file of Section II.5 proofs
• Supplement. Printout of the Proofs of Theorems in Section II.5. Print file of Section II.5 proofs
• Section II.6. Classification of Finite Groups. Section II.6 notes
• Supplement. Proofs of Theorems in Section II.6. Beamer file of Section II.6 proofs
• Supplement. Printout of the Proofs of Theorems in Section II.6. Print file of Section II.6 proofs
• Supplement. Direct Products and Semidirect Products. Direct Products and Semidirect Products notes (Contains a Cayley table of the semidirect product of ℤ₃ and ℤ₄, which is isomorphic to the dicyclic group Dic₃.)
• Supplement. Proofs of Theorems on Direct Products and Semidirect Products. Beamer file of Theorems on Direct Products and Semidirect Products
• Supplement. Printout of the Proofs of Theorems on Direct Products and Semidirect Products. Print file of Proofs of Theorems on Direct Products and Semidirect Products file
• Section II.7. Nilpotent and Solvable Groups. Section II.7 notes (Contains a proof that A_n is not solvable for n ≥ 5.)
• Supplement. Proofs of Theorems in Section II.7. Beamer file of Section II.7 proofs
• Supplement. Printout of the Proofs of Theorems in Section II.7. Print file of Section II.7 proofs
• Section II.8. Normal and Subnormal Series. Section II.8 notes
• Supplement. Proofs of Theorems in Section II.8. Beamer file of Section II.8 proofs
• Supplement. Printout of the Proofs of Theorems in Section II.8. Print file of Section II.8 proofs
• Study Guide for Chapter II

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