This chapter offers a detailed discussion of topological invariants, i.e., genus, through the lens of differential geometry, specifically, the Gauss-Bonnet theorem. Following the establishment of an understanding of genus, the next section will explain the topological continuity inherent in martensitic phase transformations, with the help of density functional calculations presented in the previous chapter. The key point is analysing the continuity of deformation within the network formed by bondings between lattice points. Martensitic phase transformations, as characterised by their diffusionless nature, are topologically continuous transformations, in contrast to other types of phase transformations. Martensitic phase transformations in NiTi and Na, along with ordinary phase transformations in Cu and Al, are employed to support this statement.