This is an introductory course in algebraic topology. Topics covered include: the fundamental group, covering spaces, singular homology, cell complexes and cellular homology and the Eilenberg-Steenrod axioms. Along the way we will introduce the basics of homological algebra and category theory.
I will produce full lecture notes, available on my website at
"Algebraic Topology" (CUP, 2002) by Hatcher is excellent and covers all the material from both Algebraic Topology I and Algebraic Topology II. You can also download it (legally!) for free from Hatcher's webpage: