In this text, the author presents a general framework for applying the standard methods from homotopy theory to the category of smooth schemes ove a reasonable base scheme $k$. He defines the homotopy category $h(\mathcal {E}_k)$ of smooth $k$-schemes and shows that it plays the same role fo smooth $k$-schemes as the ical homotopy category plays for differentiable varieties. It is shown that certain expected properties are satisfied, fo example, concerning the algebraic $K$-theory of those schemes. In this way, advanced methods of algebraic topology become available in moder algebraic geometry.