See Geometry & Topology Monographs for further study. Also consult Allen's list of recommended books on topology [.pdf].
- Hocking J.G. and Young G.S. Topology
- Kelley J.L. General Topology - "What every young analyst should know" was the originally intended title. Morse-Kelley set theory was introduced in this book.
- Steenrod N. The Topology of Fibre Bundles
- Stillwell J. Classical Topology and Combinatorial Group Theory
- Firby P.A. and Gardiner C.F. Surface Topology - One quote by Ian Stewart is sufficient. "This book is in the top ten for books conveying the dreadful secret that mathematics is fascinating."
- Gay D. Explorations in Topology: Map Coloring, Surfaces and Knots
- Ranicki A. History of Knot Theory (FREE!) - Contains dozens of historical material.
- Roberts J.D. Knots Knotes [.pdf] (FREE!)
- Bott R. and Tu L.W. Differential Forms in Algebraic Topology
- Dold A. Lectures on Algebraic Topology
- Eilenberg S. and Steenrod N.E. Foundations of Algebraic Topology
- Fulton W. Algebraic Topology: A First Course
- Hatcher A. Algebraic Topology (here for FREE!) - Very beautiful book.
- Lefschetz S. Algebraic Topology (FREE!) - Lefschetz developed new result in this monograph.
- Maunder C. R. F. Algebraic Topology
- Massey W.S. A Basic Course in Algebraic Topology
- Massey W.S. Algebraic Topology: An Introduction
- Mislin G. Algebraic Topology [.pdf] (FREE!)
- Moller J.M. Algebraic Topology Notes (FREE!)
- Munkres J.R. Elements of Algebraic Topology
- Spanier E.H. Algebraic Topology
- Switzer R.M. Algebraic Topology - Homology and Homotopy
- Vick J.W. Homology Theory: An Introduction to Algebraic Topology
- Wallace A.H. Algebraic Topology: Homology and Cohomology
- Wallace A.H. An Introduction to Algebraic Topology
- Whitehead G.H. Elements of Homotopy Theory
- Wilkins D.R. Algebraic Topology (FREE!)
- Hatcher A. Vector Bundles and K-theory (FREE!)
- Karoubi M. K-theory: An Introduction
- Rosenberg J. Algebraic K-Theory and Its Applications
- Srinivas V. Algebraic K-Theory
- Weibel C. The K-book: An Introduction to Algebraic K-theory (FREE!)
- Brin M.G. Introduction to Differential Topology [.pdf] or [.ps] here (FREE!)
- Guillemin V. and Pollack A. Differential Topology
- Hirsch M.W. Differential Topology
- Kosinski A.A. Differential Manifolds - An appendix by John W. Morgan on the work of Grigory Perelman is included in the 2007 Dover edition.
- Lang S. Introduction to Differentiable Manifolds
- Milnor J. Morse Theory - More advanced work, influential. Notes taken by M. Spivak and R. Wells.
- Milnor J.W. Topology from the Differentiable Viewpoint - As an introduction.
- Wallace A.H. Differential Topology: First Steps