The Forward Physics Facility (FPF) is a proposed suite of far-forward experiments at the Large Hadron Collider during the High Luminosity era. This Letter of Intent outlines the scientific case, experimental program, and infrastructure plans for the FPF. The FPF aims to host a comprehensive set of experiments designed to search for new physics in the far-forward region, complementing the main LHC detectors. The facility will enable precision measurements and discovery potential for a wide range of beyond-the-Standard-Model scenarios, including light and weakly-interacting particles, neutrino physics, and high-energy QCD phenomena.