  Analytic-bilinear approach for construction and study of integrable
hierarchies, in particular, the KP hierarchy is discussed. It is based on the
generalized Hirota identity. This approach allows to represent generalized
hierarchies of integrable equations in a condensed form of finite functional
equations. Resolution of these functional equations leads to the
$\tau$-function and addition formulae to it. General discrete transformations
of the $\tau$-function are presented in the determinant form. Closed one-form
and other formulae also arise naturally within the approach proposed.
Generalized KP hierarchy written in terms of different invariants of Combescure
symmetry transformations coincides with the usual KP hierarchy and the mKP
hierarchy.
