  We say that a Lie (super)algebra is ''symmetric'' if with every root (with
respect to the maximal torus) it has the opposite root of the same
multiplicity. Over algebraically closed fields of positive characteristics (up
to 7 or 11, enough to formulate a general conjecture), we computed the
cohomology corresponding to the infinitesimal deformations of all known simple
finite-dimensional symmetric Lie (super)algebras of rank $<9$, except for
superizations of the Lie algebras with ADE root systems, and queerified Lie
algebras, considered only partly. The moduli of deformations of any Lie
superalgebra constitute a supervariety. Any infinitesimal deformation given by
any odd cocycleis integrable. All deformations corresponding to odd cocycles
are new. Among new results are classifications of the cocycles describing
deforms (results of deformations) of the 29-dimensional Brown algebra in
characteristic 3, of Weisfeiler-Kac algebras and orthogonal Lie algebras
without Cartan matrix in characteristic 2. Open problems: describe
non-isomorphic deforms and equivalence classes of cohomology theories.
Appendix: For several modular analogs of complex simple Lie algebras, and
simple Lie algebras indigenous to characteristics 3 and 2, we describe the
space of cohomology with trivial coefficients. We show that the natural
multiplication in this space is very complicated.
