Abstract: This is an introductory talk. I will explain the definition of matroids and oriented matroids and give several examples. I am mostly interested in what are called ``graphic matroids'' and their duals. So, I will concentrate on that. Then, I will explain morphisms in the category of matroids and discuss the first homology of an oriented matroid. (This is the definition of H_1 of a graph without using its vertices.) The point is that you get a group MO(n) which lies between Out(F_n) and GL(n,Z). The purpose of this talk is to expose people to the fundamental definitions which are very elementary. I don't have any results yet but I want to explain what I hope to accomplish.