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In this work we present a detailed version of the paper "A Topological Invariant for Stable Map Germs" due to James Damon and Andre Galligo. In this paper, they prove that for C^∞-stable map germs which are either of ∑₂-type or of discrete algebra type (i.e. of some ∑_i-types with ly a finite number of distinct ∑_i-types near-by) the dimension of the algebra associª ted to the map germ is a topological invariant.