S. I. Agafonov and E. V. Ferapontov have introduced a construction that
allows naturally associating to a system of partial differential equations of
conservation laws a congruence of lines in an appropriate projective space. In
particular hyperbolic systems of Temple class correspond to congruences of
lines that place in planar pencils of lines. The language of Algebraic Geometry
turns out to be very natural in the study of these systems. In this article,
after recalling the definition and the basic facts on congruences of lines,
Agafonov-Ferapontov's construction is illustrated and some results of
classification for Temple systems are presented. In particular, we obtain the
classification of linear congruences in $\mathbb{P}^5$, which correspond to
some classes of $T$-systems in 4 variables.