  A polynomial transformation of the real plane $\Bbb R^2$ is a mapping $\Bbb
R^2\to\Bbb R^2$ given by two polynomials of two variables. Such a
transformation is called cubic if the degrees of its polynomials are not
greater than three. It turns out that cubic transformations are associated with
some binary and quaternary quartic forms. In the present paper these forms are
defined and studied.
