I would like to study manifolds endowed with a linear connexion $\nabla$ which is torsion free and locally flat i.e. its curvature is $0$ (such a connexion is called flat if in addition, its holonomy is trivial).

I am looking for a good reference:

to prove that such a manifold admits an atlas with affine transition maps (restriction of such maps on opens of $\mathbb{R}^n$).

to characterize the universal covering and the fundamental group of such manifolds and its link to Bieberbach groups.

Is it true that a compact affine manifold has a trivial Euler characteristic? (Chern conjecture)

Thank you for any help!