This volume is a compilation of works which, taken together, give a complete and consistent presentation of instanton calculus in non-Abelian gauge theories, as it exists now. Some of the papers reproduced are instanton classics. Among other things, they show from a historical perspective how the instanton solution has been found, the motivation behind it and how the physical meaning of instantons has been revealed. Other papers are devoted to different aspects of instanton formalism including instantons in supersymmetric gauge theories. A few unsolved problems associated with instantons are described in great detail. The papers are organized into several sections that are linked both logically and historically, accompanied by extensive comments.Contents:BPST Instantons: Discovery and Physical InterpretationCollective Coordinates and the Instanton MeasureMulti-Instanton SolutionsGreen Functions in the Instanton BackgroundFermionsConstrained Instantons, I-A Interaction and the Valley MethodSupersymmetric InstantonsReviewsReadership: High energy physicists, mathematical physicists and mathematicians.Key Features:Differs from other books on theoretical physics in its concentration on contemporary ideas of physics, rather than on its mathematical expressionAddresses those lay readers of science who are interested in the ideas of modern physics at a foundational level, as well as students (both undergraduate and graduate) and professional scientists in physics and astrophysics, with the intention of inducing further dialogue on these subjects