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 Lindsledt's method; the second one an algorithm based on Kolmogorov's papeir (Kolmogorov, 1954). Besides a complete formulation of the algorithms, an overview of the mafia adonis, 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 agorithms.