**Abstract.**

In this series of lectures we will present the construction of the Whitehead manifolds which are contractible 3-manifolds not diffeomorphic to ${\mathbb{R}}^3$. We then will describe some of the results on the geometry of these spaces such as the fact that they do not carry any metric with non positive Ricci curvature nor any metric with scalar curvature bounded away from zero. We will finish by a series of open questions on the Riemannian geometry of these spaces.

**Documents:**