  In this paper, we introduce the notions of logarithmic Poisson structure and
logarithmic principal Poisson structure; we prove that the latter induces a
representation by logarithmic derivation of the module of logarithmic Kahler
differentials; therefore, it induces a differential complex from which we
derive the notion of logarithmic Poisson cohomology. We prove that Poisson
cohomology and logarithmic Poisson cohomology are equal when the Poisson
structure is logsymplectic. We give an example of non logsymplectic but
logarithmic Poisson structure for which these cohomologies are equal. We also
give an example for which these cohomologies are different. We discuss and
modify the K. Saito definition of logarithmic forms. The notes end with an
application to a prequantization of the logarithmic Poisson algebra: (C[x; y];
{x; y} = x):
