  We make a systematic study of the focal surface of a congruence of lines in
the projective space. Using differential techniques together with techniques
from intersection theory, we reobtain in particular all the invariants of the
focal surface (degree, class, class of its hyperplane section, sectional genus
and degrees of the nodal and cuspidal curve). We study in particular the
congruences of chords to a smooth curve and the congruences of bitangents or
flexes to a smooth surface. We find that they possess unexpected components in
their focal surface, and conjecture that they are the only ones with this
property.
