The Online Books Page

Homotopy theory

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

• Topology

• Homotopy theory -- Congresses
• Homotopy theory -- Periodicals
• Homotopy equivalences
• Localization theory

• Deformations, Continuous

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

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

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

• Algebraic L-Theory and Topological Manifolds (electronic edition, 2011), by Andrew Ranicki (PDF in the UK)
• Algebraic and Geometric Surgery (electronic edition, 2010), by Andrew Ranicki (PDF in the UK)
• Exact Sequences in the Algebraic Theory of Surgery (1981), by Andrew Ranicki (PDF in the UK)
• High Dimensional Knot Theory (electronic edition, 2010), by Andrew Ranicki (PDF in the UK)
• Surgery on Compact Manifolds (second edition, ca. 1999), by C. T. C. Wall, ed. by Andrew Ranicki (PDF in the UK)

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)
• L'Analysis Situs et la Géométrie Algébrique (IN French; Paris: Gauthier-Villars et cie, 1924), by Solomon Lefschetz
  • multiple formats at archive.org
  • page images at HathiTrust; US access only

• 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)

• Quantum Topology (partial serial archives)
• 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)

• 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)

• 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)

• 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)

• 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)
• Theory of Graphs (American Mathematical Society Colloquium Publications v38, first edition; 1962), by Øystein Ore (page images at HathiTrust)
• Basic Neutrosophic Algebraic Structures and Their Application to Fuzzy and Neutrosophic Models, by W. B. Vasantha Kandasamy and Florentin Smarandache (PDF at UNM)

• 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)

• Real Variables With Basic Metric Space Topology (originally published 1993; this version c2007), by Robert B. Ash (PDF files at Wayback Machine)

• The Hauptvermutung Book: A Collection of Papers on the Topology of Manifolds (ca. 1996), ed. by Andrew Ranicki (PDF in the UK)
• Algebraic L-Theory and Topological Manifolds (electronic edition, 2011), by Andrew Ranicki (PDF in the UK)

• Noncommutative Geometry, Quantum Fields and Motives (prepublication version, ca. 2008), by Alain Connes and Matilde Marcolli (PDF at alainconnes.org)
• Lectures on Graded Differential Algebras and Noncommutative Geometry, by Michel DuBois-Violette (PDF at arxiv.org)

• Journal of Noncommutative Geometry (partial serial archives)

• Groups, Geometry and Dynamics (partial serial archives)

More items available under broader and related terms at left.