  This paper is the first of a sequence of three papers, where the concept of
an $\mathbb R$-tree dual to a measured geodesic lamination in a hyperbolic
surface is generalized to arbitrary $\mathbb R$-trees provided with a (very
small) action of the free group $F_N$ of finite rank $N\geq 2$ by isometries.
Three different definitions are given and they are proved to be equivalent. We
also describe the topology and Out$(F_N)$-action on the space of laminations.
