Any good textbook on the canonical perturbation theory for Hamiltonian systems? My teacher of classical mechanics once told us, classical mechanics is more difficult than quantum mechanics in many ways. He used the perturbation theory as an example to illustrate this point. 
So, is there any good readable textbook on the perturbation theory of classical mechanics? 
 A: Most graduate text books in Classical mechanics have (as their last two chapters) discussions of perturbation theory in classical mechanics.  These (however) are not invariably readable, and will usually restrict the solution to problems that can be described by a Hamiltonian e.g. have no friction or dissipation.  Goldstein, "Classical Mechanics" has such a chapter.  It is also possible to do problems that have dissipation, using "multiple time scale analysis", described in many mathematics texts, including Carl Bender and Steve Orzag's "Applied Mathematics for Scientists and Engineers".
Roughly (the books don't get you ready for this), this was the billion dollar problem of the 18th century, it was thought it would be possible to deduce the time if you could see where the moon was relative to the fixed stars.  If you know the time, well enough and where the sun is, you know your longitude.  And, motion of the moon is NOT adequately described by Kepler - due to the gravity of the sun and the bulge in around the earth's equator so:
Solve the relevant simple problem.  (Chapters 1-11) of a typical book.
Using the Hamilton-Jacobi equation (Chapter 13?) find a canonical transformation (Chapter 12?) to "action-angle" variables.  Angle variables don't enter the Hamiltonian of the simple model, their conjugate momenta are action variables and do enter the Hamiltonian.
Write the full Hamiltonian in terms of the action-angle variables.  Use the Hamiltonian-Jacobi transformation to find new action-angle variables (similar to the old action-angle variables) which eliminate the terms in the difference hamiltonian dependent on the angle variables and which (further) most change the motion.  And, do it until you are happy, the asymptotic series ceases to converge, or you can't do it any more.
A: The textbook by D. ter Haar is probably the best overall for its balance between physics and mathematics.  It is extensive and generally well written.  Also of note is the small "Nonlinear mechanics" by Fetter ans Walecka, which supplements their main textbook.  There is also the review paper by Chirikov which contains a good overview.
Most recent textbooks emphasize the geometrical aspect and are written by mathematicians.  Examples include the texts of Fasano and Marmi, or Jose and Saletan, or the book by Neil Rasband.  
I suppose this migration towards a more mathematical approach follows in the footsteps of the breakthrough result of KAM and the availability of computers; the combination means physicists can just compute without getting bothered by the complications and subtleties of the perturbation formalism.
