Z/pZ is a field when p is prime. That's somewhat (indirectly) related to how the RSA algorithm works, but at a high level you're doing arithmetic in Z/nZ, where

Z/pZ is a field when p is prime. That's somewhat (indirectly) related to how the RSA algorithm works, but at a high level you're doing arithmetic in Z/nZ, where n = p * q for primes p and q. Both RSA and ECC are based on the idea that exponentials are easy to compute, and undoing them is hard. In the case of RSA, you're exponentiating in Z/nZ and in ECC you're exponentiating in the group of points that arises from the chosen elliptic curve. The first book in that list is a good text. It includes an appendix that includes almost everything you need to know about projective geometry to understand the theory of elliptic curves.