  The present paper describes the $W$--geometry of the Abelian finite
non-periodic (conformal) Toda systems associated with the $B,C$ and $D$ series
of the simple Lie algebras endowed with the canonical gradation. The principal
tool here is a generalization of the classical Pl\"ucker embedding of the
$A$-case to the flag manifolds associated with the fundamental representations
of $B_n$, $C_n$ and $D_n$, and a direct proof that the corresponding K\"ahler
potentials satisfy the system of two--dimensional finite non-periodic
(conformal) Toda equations. It is shown that the $W$--geometry of the type
mentioned above coincide with the differential geometry of special holomorphic
(W) surfaces in target spaces which are submanifolds (quadrics) of $CP^N$ with
appropriate choices of $N$. In addition, these W-surfaces are defined to
satisfy quadratic holomorphic differential conditions that ensure consistency
of the generalized Pl\"ucker embedding. These conditions are automatically
fulfiled when Toda equations hold.
