  This is the second part of the revised versions of the notes of three
consecutive expository lectures given by Chongying Dong, Haisheng Li and Yi-Zhi
Huang in the conference on Monster and vertex operator algebras at the Research
Institute of Mathematical Sciences, Kyoto, September 4-9, 1994. In this part,
we discuss the commutativity, the associativity, the Jacobi identity and the
relations among them. We also discuss an analogue of endomorphism ring of a
vector space in vertex operator algebra theory.
