On first order congruences of lines in P^4 with irreducible fundamental surface

In this article we study congruences of lines in P^n, and in particular of order one. After giving general results, we obtain a complete classification in the case of P^4 in which the fundamental surface F is in fact a variety, i.e. it is integral, and the congruence is the irreducible set of the trisecant lines of F.