Publisher Summary The general theory of buckling and post-buckling behavior of elastic structures has led to a considerable amount of research in this field. A comprehensive survey provides a very useful bibliography, together with an overview of the achievements, status, and goals of post-buckling theory. The chapter provides a unified, general presentation of the basic theory in a form suitable for application to a wide variety of special problems. This will be done with the help of the succinct notation of functional analysis, which turns out to be remarkably appropriate for the purpose. Simple conceptual models can illustrate with remarkable verisimilitude many of the essential characteristics of the buckling and post-buckling behavior of more complicated structural systems. Before undertaking a general analysis of arbitrary elastic structures, such models are exploited in order to expose basic concepts of bifurcation buckling, snap buckling, imperfection-sensitivity, load-shortening relations, and stability.