  The free Banach lattice over a Banach space is introduced and analyzed. This
generalizes the concept of free Banach lattice over a set of generators, and
allows us to study the Nakano property and the density character of
non-degenerate intervals on these spaces, answering some recent questions of B.
de Pagter and A.W. Wickstead. Moreover, an example of a Banach lattice which is
weakly compactly generated as a lattice but not as a Banach space is exhibited,
thus answering a question of J. Diestel.
