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**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.