Algebraic topology

Introductory

Hutchings, Introduction to higher homotopy groups and obstruction theory

Hatcher, Algebraic topology

Munkres, Elements of algebraic topology

Munkres, Topology

May, A concise course in algebraic topology

Vasiliev, Introduction to topology

Whitehead, Elements of homotopy theory

tom Dieck, Algebraic topology

Lee, Introduction to topological manifolds

Rotman, An introduction to algebraic topology

Massey, A basic course in algebraic topology

Bott and Tu, Differential forms in algebraic topology

Intermediate

Bredon, Topology and geometry

Spanier, Algebraic topology

Strom, Modern classical homotopy theory

Davis and Kirk, Lecture notes in algebraic topology

Aguilar et al, Algebraic topology from a homotopical viewpoint

Switzer, Algebraic topology--homotopy and homology

Massey, Singular homology theory

CW complexes

Lundell and Weingram, The topology of CW complexes

Fritsch and Piccinini, Cellular structures in topology

Obstruction Theory

Baues, Obstruction theory

Model categories

Dwyer and Spalinski, Homotopy theory and model categories

May, More concise algebraic topology

Kamps and Porter, Abstract homotopy and simple homotopy theory

Riehl, Categorical homotopy theory

Hovey, Model categories

Hirschhorn, Model categories and their localization

Simplicial sets and objects

May, Simplicial objects in algebraic topology

Goerss and Jardine, Simplicial homotopy theory

Richter, From categories to homotopy theory

Higher categories

Cisinski, Higher categories and homotopical algebra

Land, Introduction to infinity-categories

Riehl and Verity, Elements of infinity-category theory

Simpson, Homotopy theory of higher categories

Lurie, Higher topos theory

Special subjects

Persistent algebraic topology and topological data analysis