# nLab homotopy theory and algebraic topology -- references

The following lists basic references on homotopy theory, algebraic topology and some $(\infty,1)$-category theory and homotopy type theory, but see these entries for more pointers.

Historical article at the origin of all these subjects:

### Topological homotopy theory

Textbook accounts of homotopy theory of topological spaces (i.e. via “point-set topology”):

### Algebraic topology

Textbooks:

On constructive methods (constructive algebraic topology):

Lecture notes:

Survey of various subjects in algebraic topology:

Survey with relation to differential topology:

Some interactive 3D demos:

Further pointers:

### Abstract homotopy theory

On localization via model category-theory:

Lecture notes:

Introduction, from category theory to (mostly abstract, simplicial) homotopy theory:

### Basic homotopy type theory

Exposition:

Textbook accounts:

For more see also at homotopy theory formalized in homotopy type theory.

### Outlook

Indications of open questions and possible future directions in algebraic topology and (stable) homotopy theory:

More regarding the sociology of the field (such as its folklore results):

Last revised on November 2, 2022 at 12:11:13. See the history of this page for a list of all contributions to it.