  Non-degenerate bilinear forms over fields of characteristic 2, in particular,
non-symmetric ones, are classified with respect to various equivalences, and
the Lie algebras preserving them are described. Although it is known that there
are two series of distinct finite simple Chevalley groups preserving the
non-degenerate symmetric bilinear forms on the space of even dimension, the
description of simple Lie algebras related to the ones that preserve these
forms is new. The classification of 1-forms is shown to be related to one of
the considered equivalences of bilinear forms. A version of the above results
for superspaces is also given.
