In this opening chapter, the structural dynamics problem is formulated for simple struc tures that can be idealized as a system with a lumped mass and a massless supporting structure. Linearly elastic structures as well as inelastic structures subjected to applied dynamic force or earthquake-induced ground motion are considered. Then four methods for solving the differential equation governing the motion of the structure are reviewed briefly. The chapter ends with an overview of how our study of the dynamic response of single-degree-of-freedom systems is organized in the chapters to follow.