Classical constructive methods in KAM theory

Two methods for constructing quasiperiodic solutions as expansion in a small parameter are discussed. The first one is the classical Lindstedtʹs method; the second one an algorithm based on Kolmogorovʹs paper (Kolmogorov, 1954). Besides a complete formulation of the algorithms, an overview of the main ideas leading to the proof of convergence of the expansions is given. Some comparison is also made, including in particular the analysis of the effectiveness of the algorithms.