I am leraning differential geometry and i have a few questions on curvature:

1.Gauss invented "Gauss curvature" to measure how surface curves.

2.Riemann gives an ingenious generalization of gauss curvature from surface to higher dimensional manifold using "Riemannian curvature tensor"(sectional curvature is exactly the gauss curvature of the image of the "sectional" tangent 2-dim subspace under exponential map)

3.In modern textbook on differential geometry,people usually first define connection and then Riemannian curvature tensor is expressed in terms of connection.

My questions are:

1.Are there some other "curvature" (besides gauss curvature and and Riemmanian curvature as its generalization) which people have invented to measure how space curves?

2.In history,who first introduced connection to describe Riemannian curvature tensor and why this idea is natural?

Thank you very much!