  We compute instanton corrections to the low energy effective prepotential of
N=2 supersymmetric theories in a variety of cases, including all classical
gauge groups and even number of fundamental matter hypermultiplets. To this
end, we take profit of a set of first- and second-order equations for the
logarithmic derivatives of the prepotential with respect to the dynamical scale
expressed in terms of Riemann's theta-function. These equations emerge in the
context of the Whitham hierarchy approach to the low-energy Seiberg--Witten
solution of supersymmetric gauge theories. Our procedure is recursive and
allows to compute the effective prepotential to arbitrary order in a remarkably
straightforward way. General expressions for up to three-instanton corrections
are given. We illustrate the method with explicit expressions for several
cases.
