apenext: A Multi-Tflops LQCD Computing Project

This paper is a slightly modified and reduced version of the proposal of the {\bf apeNEXT} project, which was submitted to DESY and INFN in spring 2000. .It presents the basic motivations and ideas of a next generation lattice QCD (LQCD) computing project, whose goal is the construction and operation of several large scale Multi-TFlops LQCD engines, providing an integrated peak performance of tens of TFlops, and a sustained (double precision) performance on key LQCD kernels of about 50% of peak speed.