Stable solutions are ubiquitous in differential equations. They represent meaningful solutions from a physical point of view and appear in many applications, including mathematical physics and geometry. This book offers a self-contained presentation of the notion of stability in elliptic partial differential equations (PDEs). The author makes unique use of the Gelfand problem as a unifying theme and utilizes stability as a central tool. He also presents many other classical techniques, such as phase plane analysis, fixed point arguments, and blow-up analysis, and modern approaches, such as...