A Mackey functor $M$ is a structure analogous tothe representation ring functor $H \mapsto R(H)$ encoding good formal behaviour under induction andrestriction. More explicitly,$M$ associates an abelian group $M(H)$ to each closed subgroup $H$ of a fixedcompact Lie group $G$, and to each inclusion $K \subseteq H$ it associates a restriction map ${\rmres}^H_K:M(H) \rightarrow M(K)$ and an induction map${\rm ind}^H_K:M(K) \rightarrow M(H)$. This paper gives ananalysis of the category of Mackey functors $M$ whose values are rational vector spaces: such a Mackey functormay be specified by giving a suitably continuous family consisting of a ${\Bbb Q} \pi_0(W_G(H))$-module $V(H)$ for each closed subgroup $H$ with restriction maps $V(\hat{K}) \rightarrow V(K)$ whenever $K$ is normal in$\hat{K}$ and $\hat{K}/K$ is a torus (a ‘continuous Weyl-toral module’). We show that the category of rationalMackey functors is equivalent to the category of rational continuousWeyl-toral modules. In Part II this willbe used to give an algebraic analysis ofthe category of rational Mackey functors, showing in particular thatit has homological dimension equal to the rank of the group.

1991 Mathematics Subject Classification:19A22, 20C99, 22E15, 55N91, 55P42, 55P91.