401-3001-61L Algebraic Topology I

Abstract	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.
Objective
Lecture notes	I will produce full lecture notes, available on my website at www.merry.io/algebraic-topology
Literature	"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: www.math.cornell.edu/%7ehatcher/AT/ATpage.html Another classic book is Spanier's "Algebraic Topology" (Springer, 1963). This book is very dense and somewhat old-fashioned, but again covers everything you could possibly want to know on the subject.
Prerequisites / Notice	You should know the basics of point-set topology (topological spaces, and what it means for a topological space to be compact or connected, etc). Some (very elementary) group theory and algebra will also be needed.