FELIX: A Full acceptance detector at the LHC: Letter of intent

The FELIX Collaboration proposes the construction of a full acceptance detector for the LHC, to be located at Intersection Region 4, and to be commissioned concurrently with the LHC. The primary mission of FELIX is the study of QCD: to provide comprehensive and definitive observations of a very broad range of strong-interaction processes. This document contains a description of the detector concept including details of the individual detector elements and their performance characteristics, an extensive discussion of the physics menu, and the plans for integration of FELIX into the collider lattice and physical environment.