Bertini studied from 1863 with a grant from his hometown at the University of Bologna, first to become an engineer with the goal but then turned under the influence of Luigi Cremona of mathematics. In 1866 he fought under Giuseppe Garibaldi in the Italian wars of independence. Then he made in 1867 graduated from the University of Pisa ( on the advice of Cremona ), and then studied further in 1868 in Milan, where his teachers Cremona had changed and where he also studied with Felice Casorati and Francesco Brioschi. Bertini was a high school teacher in 1870 in Milan and from 1872 in Rome. In 1875 he became professor of geometry in Pisa, where he returned after his time from 1880 to 1892 as a professor in Pavia where he retired in 1922.
In algebraic geometry, he continued the work of his teacher Cremona and studied the invariant theory of Cremona transformation ( unique birational pictures ), which he applied also to the resolution of the singularities of algebraic curves.
- Introduction to projective geometry of multidimensional spaces, Vienna, Seidel and Son, 1924