In our next meeting we will be discussing Safra's construction for 
determinization of Buchi automata, and alternating automata and their
non-emptiness problem.

For the Safra's construction the reference is 

S. Safra. On the complexity of $\omega$-automata. In Proceedings of 29th
 Annual Symposium on Foundations of Computer Science (FOCS'89).  
pp. 319--327. 

Of course, you only need to read the determinization part of the paper,
and can also consult Chapter 3 of the book.
 
Here's a link to an electronic version: 
http://ieeexplore.ieee.org/iel2/219/889/00021948.pdf?isNumber=889&prod=CNF&arnum
ber=21948&arSt=319&ared=327&arAuthor=Safra%2C+S.

Note that you need a subscription to IEEE Xplore to access it, i.e. you
can do this from UofT, but probably not from home. 

For alternating automata, the reference is Chapter 9 of the book + the 
notes from the model-checking course if you need them.