Ultrametric spaces are some of the nicest topological spaces there are. In this series of talks we will discuss ultrametric spaces whose distance function takes values in an arbitrary complete lattice \Gamma. We will show that the category of \Gamma-ultrametric spaces and non-expanding maps is equivalent to a full subcategory of separated presheaves on \Gamma^{op}. We will further show that under this equivalence the sheaves correspond to the spherically complete \Gamma-ultrametric spaces. After we have established this equivalence we will use it to show that theorems originally proved for \Gamma-ultrametric can be proved for sheaves. This talk is based on part of my research during this last year.