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Lecture Notes.
Lecture 1: Overview.
Lecture 2: Homotopy.
Lecture 3: CW and HEP.
Lecture 4: CW complexes and RP^n.
Lecture 5: CP^n; CW pairs have HEP.
Lecture 6: The fundamental group: definition.
Lecture 7: Path-lifting and pi_1(S^1).
Lecture 8: pi_1(S^1), functoriality, and Brouwer's theorems.
Lecture 9: The fundamental theorem of algebra; basepoint dependence.
Lecture 10: Examples and warm-up to Seifert van Kampen.
Lecture 11: Group presentations and Seifert van Kampen.
Lecture 12: Computations of pi_1.
Lectures 13-14: Application to knot theory.
Lecture 15: Covering spaces and pi_1: overview and consequences.
Lecture 16: Covering spaces and pi_1, part two.
Lecture 17: Covering spaces and pi_1, part three.
Lecture 18: Uniqueness of coverings and the universal cover.
Lecture 19: Finishing the classification theorem.
Lecture 20: Regular covers and deck transformations
Lecture 21: Introduction to higher homotopy groups.
Lecture 22: First examples of homotopy groups.
Lecture 23: pi_n(S^n) and fiber bundles.
Lecture 24: The Hopf fibration and exact sequences.
Lecture 25: Simplicial homology.
Lecture 26: Singular homology.
Lecture 27: Zeroth homology and contractible spaces.
Lecture 28: Functoriality and chain homotopies.
Lecture 29: Mayer-Vietoris and Brouwer's theorem, revisited.
Lecture 30: The homology of a surface and the long exact sequence of a pair.
Lecture 31: The Snake Lemma.
Lecture 32: The Subdivision Lemma and excision.
Lecture 33: Simplicial and singular homology agree.
Lecture 34: Eilenberg-Steenrod and cellular homology.
Lecture 35: Change of coefficients and the Euler characteristic.
Lecture 36: The Künneth formula and introduction to cohomology.
Lecture 37: Universal coefficients for cohomology and the cup product.
Lecture 38: The cap product and Poincaré duality.
Lecture 39: The cohomology of projective space and the Borsuk-Ulam theorem.
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