In this talk we present an algorithm that allows us to compute the Jumping Numbers and their corresponding Multiplier Ideals for ideals in local regular rings of dimension two. Another result that we will present is a rational formula for the Poincaré series, a series that encodes the jumping numbers and their corresponding multiplicities. This is a work in progress with Maria Alberich Carramiñana, Josep Àlvarez Montaner and Victor González Alonso.