  In this paper we show that a path-wise solution to the following integral
equation $$ Y_t = \int_0^t f(Y_t) dX_t \qquad Y_0=a \in \R^d $$ exists under
the assumption that X_t is a L\'evy process of finite p-variation for some $p
\geq1$ and that f is an $\alpha$-Lipschitz function for some alpha>p. There are
two types of solution, determined by the solution's behaviour at jump times of
the process X, one we call geometric the other forward. The geometric solution
is obtained by adding fictitious time and solving an associated integral
equation. The forward solution is derived from the geometric solution by
correcting the solution's jump behaviour. L\'evy processes, generally, have
unbounded variation. So we must use a pathwise integral different from the
Lebesgue-Stieltjes integral. When X has finite p-variation almost surely for
p<2 we use Young's integral. This is defined whenever f and g have finite p and
q-variation for 1/p+1/q>1 (and they have no common discontinuities). When p>2
we use the integral of Lyons. In order to use this integral we construct the
L\'evy area of the L\'evy process and show that it has finite (p/2)-variation
almost surely.
