• Riemann
• dissertazione inaugurale
• quaderni lezioni
• analisi complessa
• Betti

After a brief excursus on some relevant moments in the developing of Complex Function Theory, straddling over the eighteenth and the nineteenth century, we cast light on the content of Riemann's Inaugural Dissertation of 1851, who laid the foundations of modern Complex Analysis.

In 1858 Betti translated Riemann’s thesis into Italian, thus contributing to the dissemination of his ideas. The third chapter of the thesis aims at outlining the figure of Betti and the scientific fellowships that were to influence his studies. The last chapter is devoted to an analysis of some lecture notes of some courses Betti held at the University of Pisa, in which one can detect some important developments of topics, such as the connectedness of manifolds, that would become crucial in the newborn Topology.