Handbook on Plasma Instabilities, Volume 1 serves as an introduction to the field of plasma physics and plasma instabilities. Topics covered include basic plasma physics, statistical plasma theory, and magnetohydrodynamics (MHD), as well as the many-species theory and plasma containment. The motion of individual particles, oscillations and waves, and MHD instabilities of a real and an ideal plasma are also discussed. This volume is comprised of 13 chapters and begins with a survey of the various applications of plasma sciences and an overview of the fundamental concepts of plasma physics. Basic plasma physics, the physics of instabilities, orbit theory, kinetic theory, MHD, and the many-fluid theory are then presented. The following chapters focus on the principles of plasma containment and waves in plasmas, together with the basic features of plasma instabilities and their classification. The classical MHD stability theory of an ideal and of a real plasma is also described. The final chapter is devoted to drift waves and drift instabilities in inhomogeneous plasmas, paying particular attention to the theory of gradient instabilities and the microscopic theory of waves in non-homogeneous collisionless plasmas. This handbook is intended for beginners in plasma physics and plasma instabilities and for physicists and engineers working actively in the field.