## A vague description of topics covered each class:

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