One of the obstacles that arises in the generalization of Sturm’s oscillation theorem to the case of systems is the need to associate a sign with each conjugate point, necessitating a signed count rather than a direct count of such points. In 1996, Barry Simon, Gerald Teschl, and Fritz Gesztesy introduced an approach that overcomes this obstacle, which they referred to as “renormalized oscillation theory.” In this talk, I will discuss the motivation for renormalized oscillation theory, and describe how the theory can be developed through use of a topological invariant called the Maslov index.