  The first part of the book is devoted to the symmetry approach to
classification of scalar integrable evolution PDEs with two independent
variables. In the second part systems of evolution equations with polynomial
homogeneous right-hand side are considered. Such systems are associated with
associative algebras and, more generally, with non-associative algebraic
structures, whose structural constants are defined by the coefficients of the
system under consideration. We explore which structures correspond to
polynomial integrable models. Integrable systems polynomial in derivatives are
described in geometric terms. The third part we consider integrable vector
izotropic and anizotropic systems.
