Tropical Geometry is a sub-branch of algebraic geometry whose "varieties" are piecewise linear degenerations of varieties in the classical sense. A surprising number of results concerning algebraic varieties hold true for their tropical counterparts. In this talk, we will introduce varieties over the tropical semiring and give an easy method of constructing tropical curves. Following this, we will discuss tropical analogs of Bezout's Theorem, the group law on cubics, and a result of Cayley that a general plane quartic admits exactly 28 bitangent lines. If time permits, we will introduce divisors on tropical curves and state tropical analogs of the Riemann-Roch and Brill-Noether theorems. Speaker(s): Drew Ellingson (UM)