  This paper introduces a class of smooth projective varieties that generalise
and share many properties with partial flag varieties of type A. The quiver
flag variety M_\vartheta(Q,r) of a finite acyclic quiver Q (with a unique
source) and a dimension vector r is a fine moduli space of stable
representations of Q. Quiver flag varieties are Mori Dream Spaces, they are
obtained via a tower of Grassmann bundles, and their bounded derived category
of coherent sheaves is generated by a tilting bundle. We define the multigraded
linear series of a weakly exceptional sequence of locally free sheaves E =
(O_X,E_1,...,E_\rho) on a projective scheme X to be the quiver flag variety |E|
= M_\vartheta(Q,r) of a pair (Q,r) encoded by E. When each E_i is globally
generated, we obtain a morphism \phi_|E| : X -> |E| realising each E_i as the
pullback of a tautological bundle. As an application we introduce the
multigraded Plucker embedding of a quiver flag variety
