After reviewing simplicial homotopy theory, we introduce the framework of model categories. We shall give some applications of this abstract method in algebraic geometry.

Category theory. Basic algebraic geometry.

[1] Goerss-Jardin: Simplicial homotopy theory;

[2] K. Brown: Abstract homotopy theory and generalized sheaf cohomology (Trans. AMS 1973);

[3] Morel-Voevodsky: A1-homotopy theory of schemes (Pub. Math. IHES 1999).