Cesis family belonged to the aristocracy of Rome, his mother 's maiden name was Orsini. Federico received a thorough education by private teachers. Showed early interest in the natural sciences. He believed that nature should be explored by direct intuition and not - as previously customary in the universities - according to the writings of Aristotle and other ancient authors. Cesis father did not agree with the scientific ambitions of the Son, but Federico received moral and financial support for their projects through the mother.
1603, at the age of eighteen, Cesi founded the Accademia dei Lincei, which should enjoy a reputation which soon. The founding members were beside Cesi the mathematician Francesco Stelluti, the Dutch physicist, astrologer and alchemist Johannes van Heeck (* 1577) and Anastasio de Fillis. The members lived in a narrow residential community in the house Cesis. There they were, a library and modern equipment, such as already the microscope for scientific investigations.
In Rome, the Academy of the Curia and the aristocracy was regarded with suspicion, it could be assumed the member to perform black magic, they were suspected of deviation from church doctrine and suspected even the worst of their lives change. They had therefore to constantly fight against intrigues, until finally Heeck was forced to leave Rome. The other members were temporarily scattered to different place. However Cesi held with all epistolary contact.
On a trip to Naples Cesi learned scholar Giambattista della Porta know and decided to set up a branch in Naples his academy, whose member della Porta was in 1610. Other members were Cardinal Francesco Barberini, a nephew of the future Pope Urban VIII and his secretary Cassiano dal Pozzo. 1611 Galileo Galilei was a member. Some of his writings have been published by the Academy. In the same year Cesi began the project to collect the fossils found on his estate Acqua Sparta in Umbria and systematize, the first known in history of European science companies of its kind after his death, the results of Stelluti were published.
In its heyday, the Academy had 32 members. With the death of its founder in 1630 it lost its importance. After varied fortunes she was in the 19th century, first in 1840 by Pope Gregory XVI. closed, but soon revived.