Noncommutative geometry is a relatively new branch of mathematics (it was created by Alan Connes in the 80's). It has recently atracted much attention from physicists due to its appearence in superstring theories. I won't say anything about physics, though. I will explain how noncommutative spaces arises naturally as a generalisation of topological spaces. I will then focus on the algebraic category, and explain how to do geometry over noncommutative spaces. I will finish by explaining how to write down Maxwell's equations over a noncommutative spacetime.