Gauss-Bonnet Theorem

Intuitive

Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.

Concrete

A fantastic introduction that explains the Gauss-Bonnet theorem in intuitive terms is Geometry and topology in many-particle systems by Joel E. Moore

Abstract

The motto in this section is: the higher the level of abstraction, the better.

Why is it interesting?

The Gauss-Bonnet theorem is a formula that yields a topological invariant, i.e. something that can be used to characterise e.g. manifolds.