This volume looks at themes including: calculus of variations; nonlinear mechanics and ergodic theory; and approximation and asymptotics. The Krylov-Bogolubov method of averaging forms the crux of the papers included in this volume, and numerous examples of its applications are given. Bogolubov later returns to this topic to prove the existence of quasi-periodic solutions of certain mechanical systems whose number of degrees of freedom is more than one.