The Puteano Residence is the only structure surviving from the original system of university residences in Pisa. The building in on the west side of Piazza dei Cavalieri and it was completed under Ferdinando I based on Vasari's project. Between the end of the 16th and the beginning of the 17th century, in fact, the old church of San Pietro in Cortevecchia was incorporated in a single set of buildings together with three newly-built houses which took the place of the medieval buildings which were there. This new set of buildings was called San Rocco. It is an interesting example of the planning a set of houses in a series, an architectural tendency which was already well established in Lazio, Veneto and Tuscany.

The first of the three buildings beside the church was perpetually donated to be the Puteano Residence from 1604: This structure is the only one in Piazza dei Cavalieri which was not dedicated to the Knights of Saint Stephen. It was the desire of the Archbishop Carlo Antonio Dal Pozzo that the building would instead house students coming from the diocese of Biella, where the Archbishop also came from, to study at the University of Pisa.

One can still see the frescoes attributed to Michelangelo Cinganelli on the upper portion of the façade of the three-story building. Cinganelli completed these frescoes at the beginning of the 17th century, for the opening of the residence itself, decorating the building with coats of arms and heraldic symbols which allude both to the founder of the residence and the residence's role. Like the graffiti on the façade of the Palazzo della Carovana and the frescoes on the Palazzo dell'Orologio, these frescoes were to extend over the other buildings beside the residence as well, to ensure an harmonious and homogeneous scenographic effect in the square; however, only the frescoes on the façade of the Collegio Puteano were finished. They were restored at the end of the 19th century and then repeatedly up until 1969, but the majority of the decorations have been lost, as can be seen in the bare panels in the lower part of the façade.

The residence was conceded to the Scuola Normale Superiore in 1930 during the period of renewal and expansion under Gentile's directorship and thanks to negotiations with Cardinal Pietro Maffi, Archbishop of Pisa. The residence conserved the Section A, reserved by statute to seven Piedmont students, but also opened a Section B, for students at the Scuola Normale. During the fascist era students were admitted as residents there while studying political, economic and legal doctrine in the “Mussolini College for Corporative Sciences”, but during the occupation and the Anglo-American requisition of the area, the Puteano had to serve as a provisory home for students and professors exiled from the Palazzo della Carovana.

When the requisition of the Puteano residence ended, in 1945, its activity began again, and for a while it was called “Collegio Mazzini”. It was used for many purposes over the years, and after its most recent and important restoration, it is used as temporary housing for visitors. It is also the seat of the Centro di Ricerco Matematica named after the illustrious mathematician, Ennio De Giorgi. This center was founded in 2001 thanks to a collaborative effort between the Scuola Normale Superiore, the University of Pisa and the Scuola Superiore Sant'Anna.