The theme of this volume is a treatment of differential equations on a $C^infty$ manifold $V$ by separation of variables techniques. More specifically, given a Lie transformation group $L$ of $V$ and a Lie subgroup $Hsubset L$, if $D(V)$ is the set of differential operators on $V$ invariant under $L$, then the principal object of study is the set of distributions $T$ on $V$ satisfying the following two conditions: $T$ is an eigendistribution of each $Din D(V)$; and $T$ is invariant under $H$.