Plasticity plays a pivotal role in the development of most subjects covered in this book series. To assist the reader, this chapter presents some of the basic ideas behind incremental metal plasticity. A brief outline of phenomenological aspects of elastic-plastic behavior is presented at the outset, followed by a cursory review of the main stress tensor concepts required in later developments. The classical formulation of J ₂ flow theory with isotropic hardening, the main model used in the book, is described next in some detail. This is followed by a brief expos of anisotropic plasticity suitable for modeling pipe yield anisotropy. Three nonlinear kinematic hardening models used in special problems involving reverse loading are outlined next. Throughout the book, bifurcation checks in the plastic range are performed using the incremental version of the J ₂ deformation theory or its anisotropic counterpart. For this reason, a section is devoted to summarizing the basic equations of this theory. This chapter is aimed at readers with some familiarity with plasticity. The uninitiated reader is referred to more complete treatments of the subject for an in-depth understanding (e.g., see list of books in references).