The etale fundamental group is a generalization of the absolute Galois group of a field to algebraic geometry. In this talk, we'll define the etale fundamental group of a scheme and discuss a few of its basic properties. We'll explore several examples of interest to number theory and relate the etale fundamental group of a k-scheme to the absolute Galois group of k. Time permitting, we will discuss a few ways that etale fundamental groups can be used to understand the absolute Galois group of Q. Speaker(s): Patrick Lenning (UM)