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We explain a classical construction of a del Pezzo surface of degree d = 4 or5 as a smooth order two congruence of lines in 3-space whose focal surface is aquartic surface $X_{20-d}$ with 20-d ordinary double points. We also show that$X_{15}$ can be realized as a hyperplane section of theCastelnuovo-Richmond-Igusa quartic hypersurface. This leads to the proof ofrationality of the moduli space of 15-nodal quartic surfaces. We discuss someother birational models of $X_{15}$: quartic symmetroids, 5-nodal quarticsurfaces, 10-nodal sextic surfaces in $P^4$ and nonsingular surfaces of degree10 in $P^6$. Finally we study some birational involutions of a 15-nodal quarticsurface which, as it is shown in Part 2 of the paper jointly with I. Shimada,belong to a finite set of generators of the group of birational automorphismsof a general 15-nodal quartic surface.

15-nodal quartic surfaces.I: quintic del Pezzo surfaces and congruences of lines in $\bbP^3$