Algebraic Topology
Allen Hatcher
Online link
Prerequisites: Basic point-set topology, group theory, ring theory, linear algebra.
One of the most famous introductions to the subject, and the main reference for the three algebraic topology modules at Warwick (MA3F1 Introduction to Topology, MA3H6 Algebraic Topology, and MA4J7 Cohomology and Poincaré Duality). The book often relies on geometric or visual intuition in proofs which may be helpful conceptually for a first course, but can feel rather informal or otherwise difficult to generalise in many cases, particularly low-dimensional arguments. The book does not cover any differential topology.
A Quick Proof of the Seifert–Van Kampen Theorem
Andrew Putman
Online link
Prerequisites: Covering space theory.
Counterexamples in Topology
Lynn A. Steen, J. Arthur Seebach Jr.
Online link
Prerequisites: None.