Abstract: I will describe few classical variational problems related to very basic geometrical notions, such as length of curves, area of surfaces and volumes. I will give the solution of the classical isoperimetric problem and how this problem rapidly induces natural related problems which are largely open. Increasing dimension, I will show how the mean curvature of a surface becomes the key ingredient and give an overview of the classical theory of "minimal" surfaces in euclidean space. Time permitting, I will describe few applications of these theories to natural sciences, from general relativity to biology.