  Let (G,P) be a quasi-lattice ordered group and let X be a compactly aligned
product system over P of Hilbert bimodules. Under mild hypotheses we associate
to X a C*-algebra which we call the Cuntz-Nica-Pimsner algebra of X. Our
construction generalises a number of others: a sub-class of Fowler's
Cuntz-Pimsner algebras for product systems of Hilbert bimodules; Katsura's
formulation of Cuntz-Pimsner algebras of Hilbert bimodules; the C*-algebras of
finitely aligned higher-rank graphs; and Crisp and Laca's boundary quotients of
Toeplitz algebras. We show that for a large class of product systems X, the
universal representation of X in its Cuntz-Nica-Pimsner algebra is isometric.
