In this text, the author presents a general framework for applying the standard methods from homotopy theory to the category of smooth schemes over 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 for smooth \(k\)-schemes as the classical homotopy category plays for differentiable varieties. It is shown that certain expected properties are satisfied, for example, concerning the algebraic \(K\)-theory of those schemes. In this way, advanced methods of algebraic topology become available in modern algebraic geometry.