In this talk we will define and explore the concept of a class of complex numbers called periods.  We will use this concept to explain in simple and concrete terms the notion of a motivic Galois group. (Motivic Galois groups generalize the classical notion of a Galois group.  The hope is, given a suitably explicit description, that they will be as fundamental to understanding trancendental field extensions as the classical groups are to understanding finite field extensions.)  We will then show in a special case how a particular motivic Galois group can be constructed from an algebra of suitable graphs, and we will end by suggesting a possible generalization.