Lecture 1: Basic Topology and Graphs
Lecture 2: Simplicial Complexes
Lecture 3: Cell complexes
Lecture 4: Homotopy of maps
Lecture 5: Homotopy equivalence of spaces
Lecture 6: The simplicial approximation theorem
Lecture 7: The simplicial approximation theorem 2
Lecture 8: The fundamental group: Basics
Lecture 9: Functoriality of the fundamental group
Lecture 10: Edge loop group
Lecture 11: The fundamental group of the circle and the fundamental theorem of algebra
Lecture 12: Free groups: 3 definitions
Lecture 13: Free groups: Equivalence of definitions
Lecture 14: Group presentations: Basic properties
Lecture 15: Group presentations: Tietze transformations and van Dyk's lemma
Lecture 16: Free products and their universal property
Lecture 17: Push outs: Presentations and universal properties
Lecture 18: The Seifert van Kampen Theorem: Statement and applications
Lecture 19: A sketch of the proof of the Seifert van Kampen theorem
Lecture 20: Review of homework problems
Lecture 21 & 22: Covering spaces: Definitions and statement of properties
Lecture 23: Covering spaces: Proof of path lifting and uniquesness of lifts
Lecture 24: Covering spaces: Homotopy lifting and applications