Lecture 1: Topology background and Graphs
Lecture 2: Orientations on graphs, Cayley graphs and simplicial complexes
Lecture 3: More simplicial complexes
Lecture 4: Cell Complexes and homotopys of maps
Lecture 5: Homotopy equivalence of spaces
Lecture 6: The simplicial approximation theorem
Lecture 7: The fundamental group: Basics
Lecture 8: Functoriality of the fundamental group
Lecture 9: Edge loop group
Lecture 10: The fundamental group of the circle and the fundamental theorem of algebra
Lecture 11 and 12: Free groups, universal property, fundamental group of a graph and reduced words.
Lecture 13: Midterm/Review
Lecture 14: Group presentations: Basic properties
Lecture 15: Tietze Transformations
Lecture 16: Pushouts and Universal properties
Lecture 17: Proof of Seifert van Kampen Theorem
Lecture 18: Definition of covering spaces and several examples
Lecture 19: Lifting of maps to covering spaces, path lifting, uniqueness
Lecture 20
Lecture 21
Lecture 22
Lecture 23
Lecture 24
Lecture 25
Lecture 26