Reference request for curvature in Riemannian Geometry

Question

I had studied Riemannian curvature tensor, Ricci curvature and scalar curvature . I had read the properties from Do Carmo and Lee's book. But the underlined geometry is not clear to me. Like why we need to have three different notions ? What is the significance like I found in some video that Ricci curvature measures the factor by which a volume deviates that it would be in Euclidean space. But I didn't get to see why? Can anyone provide me a reference from which I can understand the underlined geometry for defining these three different notions?