In 1880, E.B. Christoffel introduced the idea of derivative of one vector field along another vector field under the coordinate transformation, which are known by Christffel symbols. In between 1880, Greogorio Ricci-Curbastro and his student Tullio Levi-Civita studied on affine connection. An affine connection is a geometrical object on a differentiable manifold which connects tangent vector field with the nearby tangent vector field. An affine connection can be deffined by many equivalent ways. In an n-dimensional manifold, (n 1); there are infinitely many affine connections. Now we shall consider the definition of affine connection and Levi-Civita connection. Skryť popis