  We give a simple proof of Kolmogorov's theorem on the persistence of a
quasiperiodic invariant torus in Hamiltonian systems. The theorem is first
reduced to a well-posed inversion problem (Herman's normal form) by switching
the frequency obstruction from one side of the conjugacy to another. Then the
proof consists in applying a simple, well suited, inverse function theorem in
the analytic category, which itself relies on the Newton algorithm and on
interpolation inequalities. A comparison with other proofs is included in
appendix.
