The quintic threefold (the zero set of a homogeneous degree 5 polynomial on CP^4) is one of the most famous examples of a Calabi Yau manifold. It is one of the most studied in the field of Enumerative Geometry. For example, how many lines are there on a Quintic threefold? In this talk we will explain some approaches to count curves on the Quintic threefold. In particular, we will try to explain the following idea: If Y is a submanifold of X, and we understand the Enumerative Geometry of X, how can we answer questions about the Enumerative Geometry of Y? We will try to explain the idea used by Andreas Gathman to compute all the genus zero Gromov-Witten invariants of the Quintic Threefold.

The talk will be self contained and will not assume any prior knowledge of Enumerative Geometry or Gromov-Witten Invariants.