The metric tensor is a second rank (specifically, it is a (2,0) tensor) tensor $g$ with components $g_{\mu\nu}=g(\hat e_\mu,\hat e_\nu)\equiv\hat e_\mu\cdot\hat e_\nu$. It therefore describes distances and angles between vectors. Curvature tensors can be derived from it. All in all, it is arguably the most important concept in .