Introduction to Algebraic Topology
N J Wildberger
Learn algebraic topology with N J Wildberger! This course explores the fundamental group using a novel approach.
More resources on Fundamental Group
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
nLab: Fundamental Group
The nLab's entry on the fundamental group, treating it from a category-theoretic viewpoint: as an automorphism group in the fundamental groupoid, with links to covering spaces, homotopy groups and higher generalizations. Best read after a standard course in algebraic topology.
Hatcher's Algebraic Topology (free PDF)
Allen Hatcher's standard graduate textbook, freely downloadable from Cornell, covering fundamental groups, homology, cohomology and homotopy theory, with CW complexes introduced in Chapter 0 and used throughout. Readers learn to build spaces from cells and compute their algebraic invariants.
Topology
James Munkres's standard textbook on topology, in two parts: general point-set topology (spaces, continuity, connectedness, compactness, countability and separation axioms) and introductory algebraic topology, including the fundamental group, covering spaces and the Seifert-van Kampen theorem. Proof-based; suits readers comfortable with real analysis.
nLab
Collaborative wiki for mathematics, physics and philosophy written from a category-theoretic viewpoint, with cross-linked entries on categories, functors, adjunctions, topos theory, higher category theory and homotopy theory. Readers can look up precise definitions, examples and references for advanced structural mathematics.