In this thesis, we introduce the K groups of a scheme. One of the motivations for the definition of the K groups is to prove a generalized version of the Riemann-Roch Theorem. We introduce the K groups of a scheme and several constructions on them. We descrive geometric notions such as intersections and self-intersections in terms of the K groups, and later we use these notions to construct filtrations, the topological filtration on the G group and the gamma filtration on the K group, to eventually construct a replacement for the cohomology, which can be used to define the Chern character and the Todd class, the necessary ingredients to state the Grothendieck-Riemann-Roch Theorem.