The partition function is one of the key objects in statistical mechanics encoding the macroscopic behavior of the underlying models. In 1967, Kasteleyn, and independently by Fisher and Temperley, gave an explicit computation of the partition function for the dimer models on the square lattice as the determinant of the signed adjacency matrix. In this talk, I will introduce the notion of Kasteleyn matrix for the infinite, bipartite planar graphs with Z^2-periodic property, the height function of dimer covers and how the two objects related. Understanding these objects will be crucial for constructing invariant Gibbs measure and the phase diagram of the Gibbs measures for dimers on a particular graph, represented by the amoeba. This is the first talk in a series of 3 talks on the paper "Dimer and Amoeba" by Kenyon-Okounkov-Sheffield and (if time allowed) the correspondence between amoeba and the arctic curves from the T-system dimer model.