The Online Books Page

Algebraic topology

See also what's at Wikipedia, your library, or elsewhere.

• Topology

• Algebraic topology -- Congresses
• Algebraic topology -- Periodicals
• Fiber spaces (Mathematics)
• Homology theory
• Hopf algebras
• K-theory
• Low-dimensional topology
• Measure theory

• Algebraic Topology (c2002), by Allen Hatcher (PDF files with commentary at Cornell)
• Modern Algebraic Topology (New York, Macmillan; London: Collier-Macmillan, c1963), by D. G. Bourgin (page images at HathiTrust)
• A Concise Course in Algebraic Topology (electronic edition, with errata corrected), by J. Peter May (PDF at Chicago)

• Algebraic and Geometric Topology (proceedings of a 1983 conference at Rutgers; published 1984), ed. by Andrew Ranicki, N. Levitt, and F. Quinn (PDF and DjVu files in the UK)

• Exotic Homology Manifolds, Oberwolfach 2003 (prepublication version, ca. 2006), ed. by F. Quinn and Andrew Ranicki (PDF in the UK)

• Algebraic and Geometric Topology (issues more than 5 years old free to read online) (partial serial archives)

• Homology, Homotopy and Applications (volumes more than 4 years old are free to read) (partial serial archives)

• Gauge Theory for Fiber Bundles (1991), by Peter W. Michor (PDF in Austria)

• Precise Spectral Asymptotics for Elliptic Operators Acting in Fiberings over Manifolds With Boundary (1984), by Victor Ivrii (DjVu at Toronto)

• Toposes, Triples, and Theories (version 1.1, reprinted in Theory and Applications of Categories, 2005), by Michael Barr and Charles Wells (PDF in Canada)
• Category Theory for the Sciences (Cambridge, MA, and London: MIT Press, c2014), by David I. Spivak (illustrated HTML with commentary at MIT Press)
• Category Theory for Computing Science (revised reprint from Theory and Applications of Categories, 2013), by Michael Barr and Charles Wells (PDF in Canada)
• Functors and Categories of Banach Spaces: Tensor Products, Operator Ideals, and Functors on Categories of Banach Spaces (c1978), by Peter W. Michor (PDF in Austria)
• Banach Modules and Functors on Categories of Banach Spaces (c1979), by Johann Cigler, Viktor Losert, and Peter W. Michor (PDF in Austria)
• Category Theory for Programmers (free online edition), by Bartosz Milewski, ed. by Igal Tabacnik (illustrated HTML and PDF with commentary at bartoszmilewski.com and Github)

• Noncommutative Localization in Algebra and Topology (electronic edition, ca. 2006), ed. by Andrew Ranicki (PDF in the UK)

• Theory and Applications of Categories (1995-) (full serial archives)

• Algebraic L-Theory and Topological Manifolds (electronic edition, 2011), by Andrew Ranicki (PDF in the UK)

• Toposes, Triples, and Theories (version 1.1, reprinted in Theory and Applications of Categories, 2005), by Michael Barr and Charles Wells (PDF in Canada)

• Toposes, Triples, and Theories (version 1.1, reprinted in Theory and Applications of Categories, 2005), by Michael Barr and Charles Wells (PDF in Canada)

• Functors and Categories of Banach Spaces: Tensor Products, Operator Ideals, and Functors on Categories of Banach Spaces (c1978), by Peter W. Michor (PDF in Austria)

• Lower K- and L-Theory (electronic edition, 2001), by Andrew Ranicki (PDF in the UK)

• New Directions in Hopf Algebras (2002), ed. by Susan Montgomery and Hans-Jürgen Schneider (PDF files with commentary at msri.org)

• High Dimensional Knot Theory (electronic edition, 2010), by Andrew Ranicki (PDF in the UK)

• Entropy and Information Theory (electronic edition, 2000), by Robert M. Gray (PDF at Stanford)

• Homogeneous Boltzmann Equation in Quantum Relativistic Kinetic Theory (EJDE monograph #4, 2003), by Miguel Escobedo, Stéphane Mischler, and Manuel A. Valle (PDF with commentary at ams.org)

• Precise Spectral Asymptotics for Elliptic Operators Acting in Fiberings over Manifolds With Boundary (1984), by Victor Ivrii (DjVu at Toronto)
• Chebyshev and Fourier Spectral Methods (second edition), by John P. Boyd (PDF with commentary at Citeseer)

Items below (if any) are from related and broader terms.

• Geometric Topology: Localization, Periodicity and Galois Symmetry (The 1970 MIT Notes) (electronic edition, ca. 2005), by Dennis Sullivan, ed. by Andrew Ranicki (PDF in the UK)
• Open Problems in Topology (1990), ed. by J. van Mill and George M. Reed (PDF at Elsevier)
• Functional Analysis and Semi-Groups (New York: American Mathematical Society, 1948), by Einar Hille (multiple formats at archive.org)
• Algebraic Topology (American Mathematical Society Colloquium Publications v27; c1942), by Solomon Lefschetz (page images at HathiTrust)
• Analytic Topology (American Mathematical Society Colloquium Publications v28; 1942), by Gordon Thomas Whyburn (page images at HathiTrust)
• Topology (American Mathematical Society Colloquium Publications v12; 1930), by Solomon Lefschetz (page images at HathiTrust)

• Algebraic and Geometric Topology (proceedings of a 1983 conference at Rutgers; published 1984), ed. by Andrew Ranicki, N. Levitt, and F. Quinn (PDF and DjVu files in the UK)
• Noncommutative Localization in Algebra and Topology (electronic edition, ca. 2006), ed. by Andrew Ranicki (PDF in the UK)

• Topology (full serial archives)
• Algebraic and Geometric Topology (issues more than 5 years old free to read online) (partial serial archives)
• Geometry and Topology (issues more than 5 years old are open access) (partial serial archives)

• Topology: A Categorical Approach (Cambridge, MA: MIT Press, 2020), by Tai-Danae Bradley, Tyler Bryson, and John Terilla (PDF files with commentary at pubpub.org)

• Banach Modules and Functors on Categories of Banach Spaces (c1979), by Johann Cigler, Viktor Losert, and Peter W. Michor (PDF in Austria)
• Functors and Categories of Banach Spaces: Tensor Products, Operator Ideals, and Functors on Categories of Banach Spaces (c1978), by Peter W. Michor (PDF in Austria)

• The Compleat Strategyst: Being a Primer on the Theory of Games of Strategy (revised edition, c1966), by J. D. Williams (PDF with commentary at rand.org)
• Games of Strategy: Theory and Applications (1961), by Melvin Dresher (PDF with commentary at rand.org)

• Graph Theory (free electronic edition, 2016), by Reinhard Diestel (PDF files at graph-theory.com)
• Basic Neutrosophic Algebraic Structures and Their Application to Fuzzy and Neutrosophic Models, by W. B. Vasantha Kandasamy and Florentin Smarandache (PDF at UNM)

• Homotopy Type Theory: Univalent Foundations of Mathematics (c2013), by Univalent Foundations Program, Institute for Advanced Study (PDF with commentary at homotopytypetheory.org)

• Lattice Theory (American Mathematical Society Colloquium Publications v25, revised edition; 1948), by Garrett Birkhoff (page images at HathiTrust)

• Surgery on Compact Manifolds (second edition, ca. 1999), by C. T. C. Wall, ed. by Andrew Ranicki (PDF in the UK)
• Invariance Theory, the Heat Equation, and the Atiyah-Singer Index Theorem (1984), by Peter B. Gilkey (Postscript files at emis.de)

• The Contraction Mapping Principle and Some Applications (EJDE monograph #9, 2009), by R. M. Brooks and Klaus Schmitt (PDF with commentary at ams.org)
• Elementary Divisors and Some Properties of the Lyapunov Mapping X to AX + XA* (Argonne, IL: Argonne National Laboratory, 1961), by Wallace Givens (page images at HathiTrust)

More items available under broader and related terms at left.