There are many good introductions to multiparty cryptography available online. Before going to the surveys, it is worth taking a look at Blum’s 1983 paper, “Coin flipping by telephone“, which is a great read and a good introduction to the difficulties one faces when one doesn’t trust one’s interlocutor! 

For an extensive treatment, we can recommend Oded Goldreich’s “Foundations of cryptography: a primer“, which gives extensive discussion of the setup, security notions, and examples. A more focused but sometimes more precise account is given in the introduction by Lindell and Pinkas, “Secure multiparty computation for privacypreserving data mining“.

For quantum protocols there is unfortunately no good general resource available. You can find specific pointers in the lecture notes. A thorough account to some of the difficulties faced when trying to come up with the right security definitions in the quantum setting can be found in a relatively recent paper by Unruh, “Universally composable quantum multi-party computation“.