This volume contains the proceedings of the first Graduate Summer School on Computational Physics on ''Finite Elements in Physics'', organised by the Computational Physics Group of the European Physical Society (EPS). The main idea of these graduate courses is to present physicists with a specific numerical domain, starting from basic theory and moving to the more advanced applications. The proceedings present a basic course on the finite element method and include descriptions of all the 1 and 2 dimensional triangular and quadrangular linear quadratic and cubic conforming elements with their convergence properties. Furthermore it also includes: - the applications of the finite element method to physical situations; - a discussion on the finite element methods for hyperbolic equations; - the state of the art of solving the Schrouml;dinger equation by a finite element approach; - methods used to compute ideal magnetohydrodynamic equilibria, linear stability and boundary elements in the domain of thermonuclear fusion research; - practical applications of finite elements in physics in the domains of plasma physics, materials science and turbulence; - algorithms to solve the matrix problems arising from finite element approaches; - an introduction to the treatment of nonlinear partial differential equations by a continuation method.