Variational and perturbation methods, together with their hybrids, are the most widely used techniques employed by applied mathematicians, physical scientists and engineers. This book presents the topic as a unified and coherent discipline encompassing the problem specific procedures. Usable results are deduced, rigorously increasing their clarity, reliability and scope of their applications. The concepts are developed from the premise assuming that the background of the reader is one expected of an advanced undergraduate student in scientific and applied mathematics discipline and is presumed to increase the accessibility and appeal to students and researchers in a broad range of areas. In this text, material scattered in literature is collected together and a number of results available so far only in the journal papers and specialised monographs included. The concepts and their contents are illustrated with comments and examples to facilitate their comprehension. The results and techniques to exploit them are illustrated by a copious use of worked out examples from a broad range of disciplines, constituting about half of the volume. The examples are selected to illustrate the applications of the results, each to a class of problems. A discerning reader can use suitable results and techniques illustrated in this text to solve a specific problem encountered. The applications part is aimed at filling the void between the foundational and the computational literature.