(... to be written)
Pseudorandom Functions are very well covered in [FOC, Volume 1, Section 3.6] and even more so in [KL15].
A good introduction to PRFs and PRPs is Iftach Haitner's talk "Pseudorandom Functions and Permutations" (slides) at the 4th BIU Winter School on Cryptography:
Another lecture that covers PRFs is Vinod Vaikuntanathan's talk "L7: Pseudorandom Functions", starting at 24:30, of an advanced course:
- [FOC] Oded Goldreich: Foundations of Cryptography, Volumes 1 and 2.
- [KL15] Jonathan Katz and Yehuda Lindell: Introduction to Modern Cryptography, 2nd Edition.
- [BS] Dan Boneh and Victor Shoup: A Graduate Course in Applied Cryptography (draft 0.4).