  A construction of general solutions of the \hbar-dependent Toda hierarchy is
presented. The construction is based on a Riemann-Hilbert problem for the pairs
(L,M) and (\bar L,\bar M) of Lax and Orlov-Schulman operators. This
Riemann-Hilbert problem is translated to the language of the dressing operators
W and \bar W. The dressing operators are set in an exponential form as W =
e^{X/\hbar} and \bar W = e^{\phi/\hbar}e^{\bar X/\hbar}, and the auxiliary
operators X,\bar X and the function \phi are assumed to have \hbar-expansions X
= X_0 + \hbar X_1 + ..., \bar X = \bar X_0 + \hbar\bar X_1 + ... and \phi =
\phi_0 + \hbar\phi_1 + .... The coefficients of these expansions turn out to
satisfy a set of recursion relations. X,\bar X and \phi are recursively
determined by these relations. Moreover, the associated wave functions are
shown to have the WKB form \Psi = e^{S/\hbar} and \bar\Psi = e^{\bar S/\hbar},
which leads to an \hbar-expansion of the logarithm of the tau function.
