This is Villa Falconieri, previously known as Villa Rufina. It was built by Monsignor Alessandro Rufini, and later expanded by Pope Paul III.
In the 17th century, it was purchased by Orazio Falconieri, who commissioned Francesco Borromini to renovate it.
Besides Borromini, the villa was also renovated by Antonio da Sangallo the Younger.
In 1921, the Villa was expropriated by Italian State.
During World War II it was damaged by bombing, but later masterly restored.
Today it houses the Vivarium Novum Latin academy.