We covered a lot in the last two lectures. Here is some attempt to give you background materials for what may not have been said in the lectures, or what was said but not written explicitly on the board. Note: the links below are suggested reading, but not assigned reading.
ECB Mode can be found in sec 7.2.2 of MOV (pages 228-230). CBC Mode is discussed also in this section (page 230). No proofs of security are given.
A good overview of provable security is Mihir Bellare's survey on practice-oriented provably security.
Hash functions are discussed in Ch. 9 of MOV. The most-used cryptographic hash function is probably SHA-1, which is a Merkle-Damgard hash function standardized by the US government.