  We introduce endo-permutation Mackey functors and the Mackey-Dade group of a
$p$-group and study their basic properties. We exhibit relations between the
Mackey-Dade group of a finite $p$-group $P$ and the Dade groups of the Weyl
groups of all subgroups of $P$. As a result, we show that the Mackey-Dade group
tensored with $\mathbb Q$ over $\mathbb Z$ is the kernel of the linearization
map for Mackey functors, introduced by the author.
