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Algebraic Topology by Michael Starbird
Much of topology is aimed at exploring abstract versions of geometrical objects in our world. The concept of geometrical abstraction dates back at least to the time of Euclid. All of the objects that we will study in this note will be subsets of the Euclidean spaces. Topics covered includes: 2-manifolds, Fundamental group and covering spaces, Homology, Point-Set Topology, Group Theory, Graph Theory and The Jordan Curve Theorem.
Author(s): Michael Starbird
127 Pages 
Algebraic topology of C algebras
This note contains below topics, Gelfand category and Gelfand functor, Gelfand space and Ktheory, Algebraic topology of the noncommutative torus, Hausdorff blowingup, Groupoids foliations and their coverings, Gelfand spaces of continuous trace C algebras, Appendices, Category theory, Topology, Lattices and filters, Sheaves and cohomology, C algebras, Continuous trace C algebras, C algebras of groupoids, Noncommutative torus Tn.
Author(s): Petr Ivankov
119 Pages
Algebraic Topology for Data Scientists
This book contains below topics, Point Set Topology Background, Abstract Algebra Background, Traditional Homology Theory, Persistent Homology, Related Techniques, Some Unfinished Ideas, Cohomology, Homotopy Theory, Obstruction Theory, Steenrod Squares and Reduced Powers, Homotopy Groups of Spheres.
Author(s): Michael S. Postol
324 Pages
Lecture Notes in Algebraic Topology
This note explains the following topics, Chain Complexes, Homology, and Cohomology, Homological Algebra, Products, Fiber Bundles, Homology with Local Coefficients, Fibrations, Cofibrations and Homotopy Groups, Obstruction Theory and EilenbergMacLane Spaces, Bordism, Spectra, and Generalized Homology, Spectral Sequences.
Author(s): James F. Davis and Paul Kirk
392 Pages
Lectures on Algebraic Topology by Haynes Miller
This PDF Lectures covers the following topics related to Algebraic Topology, Singular homology, Introduction, singular simplices and chains, Homology, Categories, functors, and natural transformations, Basic homotopy theory, The homotopy theory of CW complexes, Vector bundles and principal bundles, Spectral sequences and Serre classes, Characteristic classes, Steenrod operations, and cobordism.
Author(s): Haynes Miller
307 Pages
Algebraic Topology A Comprehensive Introduction
This book explains the following topics, Introduction, Fundamental group, Classification of compact surfaces, Covering spaces, Homology, Basics of Cohomology, Cup Product in Cohomology, Poincaré Duality, Basics of Homotopy Theory, Spectral Sequences. Applications, Fiber bundles, Classifying spaces, Applications, Vector Bundles, Characteristic classes, Cobordism, Applications.
Author(s): Laurentiu Maxim, University of Wisconsin-Madison
318 Pages
Notes On The Course Algebraic Topology
This note covers the following topics, Important examples of topological spaces, Constructions, Homotopy and homotopy equivalence, CW complexes and homotopy, Fundamental group, Covering spaces, Higher homotopy groups, Fiber bundles, Suspension Theorem and Whitehead product, Homotopy groups of CW complexes, Homology groups, Homology groups of CW complexes, Homology with coefficients and cohomology groups, Cap product and the Poincare duality, Elementary obstruction theory.
Author(s): Boris Botvinnik
181 Pages
Algebraic Topology by Andreas Kriegl
This note explains the following topics, Building blocks and homeomorphy, Homotopy, Simplicial Complexes, CWSpaces, Fundamental Group, Coverings, Simplicial Homology and Singular Homology.
Author(s): Andreas Kriegl
125 Pages
Algebraic Topology by Cornell University
This note covers the following topics, moduli space of flat symplectic surface bundles, Cohomology of the Classifying Spaces of Projective Unitary Groups, covering type of a space, A Maytype spectral sequence for higher topological Hochschild homology, topological Hochschild homology of the K 1 local sphere, QuasiElliptic Cohomology and its Power Operations, Local and global coincidence homology classes, Tangent categories of algebras over operads, Automorphisms of the little disks operad with ptorsion coefficients.
Author(s): Cornell University
NA Pages