The main goal of the thesis is to classify some particular Poisson structures, called b-Poisson, following results of Guillemin-Miranda-Pirés and Radko. To understand these results, this thesis contains some chapters of introduction to Poisson Geometry and Symplectic Geometry. There is also a new result extending the classification of Poisson structures to the non-orientable case. Moreover it is explained a way to obtain local classification of some Poisson structures that can lead to more original results.