I have started an attempt to self-study Riemannian Geometry.
I well understand all the algebraic properties of the Riemann tensor (With a symmetric connection), and how it gradually becomes less and less frightening.
However, I'm having trouble converting all the properties of this tensor into an explanation of how it represents curvature, and the same goes for the derived Ricci tensor. This is essentially what I'm aiming for in writing this question.
I can decompose this question into a set of concrete questions, but I think it is too "early" to ask them with regards to my understanding of the subject.
A Reference to relevant material would suffice.