This talk is a continuation of my talk last semester about Groebner bases and initial ideals. We will begin by reviewing initial ideals in the classical setting and then define initial forms and initial ideals with weights and valuations. We will talk about properties of initial ideals and lifting elements of the initial ideal for both total monomial orders and weights and then define the Groebner complex, tropical bases and universal Groebner bases. We will explicitly compute the Groebner complex in a few examples. If time permits, I will talk more about connections to tropical geometry. Speaker(s): Shelby Cox (University of Michigan)