Just looking for a brief explanation of what cryptography is used and where/how it is used in Monero. Thanks :)
This Wiki article on CryptoNote explains it better than anyone could do in the confines of a Stackexchange reply.
The Proof-of-Work algorithm is called CryptoNight and has several distinct differences/improvements over the earlier SHA256 algorithm used by Bitcoin and clones.
edit: This looks more like an actual specification