## A vague description of topics covered each class with tentative schedule:

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