Геометрия в Италии в первой половине XX века. Geometry in Italy in the first half of the 20th century

The article is devoted to the development of the italian schools of the projective differential geometry of G. Fubini, C. Segre, A. Terracini. The theory of differen-tial forms and the first rigidity theorem of G. Fubini, the questions of С. Segre’s tangents, the classification of secant–defective and tangent-defective varieties of A. Terracini, as well as their evolution and influence on the development of actual problems of the projective differential geometry are considered.