The book is well written and may be used by graduate students and researchers in both mechanics and applied mathematics. – Zentralblatt MATH, 1055 This book should be very useful to scientists interested in efficient approximation methods for solutions of ordinary differential equations with good accuracy, with a substantial portion devoted to celestial mechanics. It should also be interesting to theorists and applied scientists, since it gives estimates on the proximity of solutions of non-integrable problems to solutions of averaged systems that my be fully integrated. .. This book includes] examples of iterative processes and their convergence, especially useful for computer programming, either numerical or symbolic. – Mathematical Reviews, Issue 2005dAsymptotic Methods in Resonance Analytical Dynamics presents new asymptotic methods for the analysis and construction of solutions (mainly periodic and quasiperiodic) of differential equations with small parameters. Along with some background material and theory behind these methods, the authors also consider a variety of problems and applications in nonlinear mechanics and oscillation theory. The methods examined are based on two types: the generalized averaging technique of Krylov-Bogolubov and the numeric-analytical iterations of Lyapunov-Poincare. This text provides a useful source of reference for postgraduates and researchers working in this area of applied mathematics.