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We extend the well-known theory of s-numbers of linear operators to homogeneous polynomials defined between Banach spaces. Approximation, Kolmogorov and Gelfand numbers of polynomials are introduced and some well-known results of the linear and multilinear settings are obtained for homogeneous polynomials. We extend the measure of non compactness notion to the polynomial setting, and then characterize compactness of homogeneous polynomials in terms of these numbers. As an application, we study diagonal polynomials between sequence spaces. This is a part of the paper: ''Compactness and s-Numbers for polynomials'' by E. Çalışkan and P. Rueda to appear in somewhere else.