Fix a field, and consider the free abelian group on isomorphism classes of varieties over that field, modulo the relation [Y] + [X - Y] = [X] whenever Y is a closed subvariety of X. Declare multiplication to be Cartesian product, and you have the Grothendieck ring of varieties. Despite its simple definition, the Grothendieck ring turns out to have many interesting properties. For instance, if X is smooth and projective, the class [X] of X in the Grothendieck ring "knows" many numerical invariants of X, such as the Betti numbers or the Hodge numbers. In this talk, I will give an introduction to the Grothendieck ring of varieties, and explain some of the key methods for understanding the structure of this large and mysterious ring. Speaker(s): James Hotchkiss (UM)