He studied in Pavia with F. Bordoni and F. Brioschi. Cremona was politically engaged in activities connected with Italian Risorgimento. After the Italian unity (1860) he became also Senatore in the Italian parliament, and, in 1868, minister of public instruction. With Betti, Brioschi and Casorati he has always been considered the founder of modern Italian mathematical school.

In 1860 he was appointed to first Italian chair of higher geometry at the University of Bologna, where he taught until 1867, when he was called to organize with Brioschi the new born Polytechnical University of Milano. Considered as the most important organizer among Italian scientists, after the liberation of Roma (since 1873), he went to Roma to set up the schools of mathematics and engeenering.

He was a member of the Accademia Nazionale dei Lincei. He is the main forerunner of Italian school of algebraic geometry, and he was the first to understand clearly the role of birational transformations (which after him were also called Cremonian transformations) in this field.

Among his many students we cite: E. Bertini, R. De Paolis, G. B. Guccia, E. Caporali, G. Veronese, D. Montesano, but many others were directly or indirectily influenced by him.

His collected works were published in 3 vol. in 1914-17 (Hoepli, Milano)

Main commemorations and studies: E. Bertini, in Opere, III vol; G. Loria, Bibliotheca Math., 1904, 125-195; L. Berzolari, Rend. del R. Ist. Lombardo di Scienze e Lettere, (2), 39, 1906, 95-155; G. Castelnuovo, Rend. della R. Acc. Nazionale dei Lincei, (5), 12, 1930, 613-618 and Mem. della Soc. It. delle Scienze detta dei XL, 23, 1929, 25-30; G. Prasad, in Some great mathematicians of the nineteenth century, Benares, 1934, 116-143; S. Greitzer, Dictionary of Scientific Biographies, 3, 467-469.