Calculus of Variations and Partial Differential Equations : Topics on Geometrical Evolution Problems and Degree Theory The link between Calculus of Variations and Partial Differential Equations has always been strong because variational problems produce via their Euler Lagrange equation a differential equation and conversely a differential equation can often be studied by variational methods. At the summer school in Pisa in September 1996 Luigi Ambrosio and Norman Dancer each gave a course on a classical topic (the geometric problem of evolution of a surface by mean curvature and degree theory with applications to pdes resp.) in a self contained presentation accessible to PhD students bridging the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts and nicely illustrates the 2 way interaction of problems and methods. Each of the courses is augmented and complemented by additional short chapters by other authors describing current research problems and results