The main aim of this chapter is to present both an "analytical" and an "internal" reading of Husserl's Doppelvortrag, the lecture he presented to the Mathematische Gesellschaft in Göttingen in the winter semester of 1901/02. We will propose a formal reconstruction of some of the main results contained in the Doppelvortrag wherever a mathematical definition of the concepts helps to clarify Husserl's own ideas.