Corrado Segre studied at Turin under Enrico D'Ovidio. Gino Loria, who was to write famous texts on the history of mathematics, was a fellow student of Segre's and they remained friends throughout their lives. In 1883 Segre was awarded his doctorate for a thesis on quadrics in higher dimensional spaces and was appointed as an assistant to the professor of algebra and to the professor of geometry at Turin. In 1885 he was appointed as assistant in descriptive geometry.
In 1888 Segre succeeded D'Ovidio to the chair of higher geometry in Turin and he continued to hold this post for the next 36 years until his death.
Plücker's ideas on the geometry of ruled surfaces had been extended by Klein, and D'Ovidio lectured on this topic in session 1881-82. D'Ovidio also included in these lectures results of Veronese on projective geometry and of Weierstrass on bilinear and quadratic forms. This must have been a truly inspiring lecture course by D'Ovidio since it set the scene for all of Segre's research. He spent the rest of his working life on problems which arose directly or indirectly from this lecture course.
Before Segre had written his thesis he submitted a joint paper with Loria to Mathematische Annalen. It was published in 1883 but perhaps the most important outcome was that the paper greatly interested Klein who then began to correspond with Segre, a correspondence which was to continue over many years.
Segre worked on geometric properties invariant under linear transformations, algebraic curves and ruled surfaces studying transformations already considered by Brill, Clebsch, Gordan and Max Noether. In  P Speziale says that through this work of Segre's:-
... it thus became possible to reduce the classification of surfaces to that of curves. The insufficiencies of the earlier theories proposed by A Möbius, Grassmann, Cayley and Cremona were thus soon revealed.
Using the methods which he had introduced, Segre was able to study Kummer's surface in a much simpler way. This surface, which had been discovered by Kummer in 1864, is a fourth order surface with sixteen double points. In a paper published in 1896, Segre found an invariant of surfaces under birational transformations which had appeared in a different form in a 1871 article by Zeuthen: this invariant is now called the Zeuthen-Segre invariant.
In 1890 Segre looked at properties of the Riemann sphere and was led to a new area of representing complex points in geometry. He introduced bicomplex points into geometry. Motivated by the works of von Staudt, Segre considered a different type of complex geometry in 1912.
Among other important work which Segre produced was an extension of ideas of Darboux on surfaces defined by certain differential equations.
In  his clarity of writing is mentioned and illustrated with these comments:-
Segre wrote a long article on hyperspaces for the Encyklopädie der mathematischen Wissenschaften, containing all that was then known about such spaces. A model article, it is notable for its clarity and elegance.
Finally we quote the summary of Segre's importance as described in the  article:-
Through his teaching and publications, Segre played an important role in reviving an interest in geometry in Italy. His reputation and the new ideas he presented in his courses attracted many Italian and foreign students to Turin. Segre's contribution to the knowledge of space assures him a place after Cremona in the ranks of the most illustrious members of the new Italian school of geometry.
Article by: J J O'Connor and E F Robertson