A lack of coordinates makes dierentiating vector elds on manifolds depending on a choice of connection. We discuss how most connection introduce curvature and experience it rst hand. We discuss how curvature leads to holonomy. For Riemannian manifolds we introduce the classication of holonomy groups due to Berger and deRham. If time permits we conclude with submersion results in the case of non-vanishing skew-torsion.