Random graph theory is an active area of research which combines 
combinatorics, probability and graph theory. The subject began in 1960 
with monumental paper "on the evolution of random graphs" by Erdos and 
Renyi. A variety of models have been proposed for random graphs with a 
whole lot of interesting results in each of them. Examples are: G(n,p), 
random graphs in metric spaces, random graphs with degree distributions.

In this talk, I will focus on G(n,p) and talk about the connectivity 
results in it. If time permits then i would also talk about the model with 
given degree distributions.