A matroid is an abstraction of mathematical problems involving independence and overlap. Matroid structures occur in surprisingly disparate areas of mathematics including linear and abstract algebra, finite geometry, combinatorics, and topology. Moreover, general results about matroids and matroid invariants often specialize in a meaningful way to each of these cases.
Unfortunately, matroids can also be frustratingly abstract and there are an absurd number of non-trivially equivalent definitions of a matroid, making matroid theory a challenging subject to begin learning about. In this talk, I will attempt to circumvent these obstacles in order to give an accessible and motivated introduction to matroids, with examples from some of the many areas of math in which they appear.