Introduction to the hyperdeterminant and to the rank of multidimensional matrices

This is an introduction to the hyperderminant, according to Gelfand, Kapranov and Zelevinsky. The "triangle inequality", characterizing the Segre varieties such that their dual variety is a hypersurface, is proved in a geometric way (Theorems 3.3 and 6.2). Significant emphasis is given to boundary format case, to pencil of quadrics and to the rank of multidimensional matrices. In the last section we propose three open problems.