In this Letter of Intent (LOI) we propose the construction of MATHUSLA (MAssive Timing Hodoscope for Ultra-Stable neutraL pArticles) [1], a dedicated large-volume displaced vertex detector for the HL-LHC on the surface above ATLAS or CMS. Such a detector, which can be built using existing technologies with a reasonable budget in time for the HL-LHC upgrade, could search for neutral long-lived particles (LLPs) with up to several orders of magnitude better sensitivity than ATLAS or CMS, while

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... acting as a cutting-edge cosmic ray telescope at CERN to explore many open questions in cosmic ray and astro-particle physics. We review the physics motivations for MATHUSLA and summarize its LLP reach for several different possible detector geometries, as well as outline the cosmic ray physics program. We present several updated background studies for MATHUSLA, which help inform a first detector-design concept utilizing modular construction with Resistive Plate Chambers (RPCs) as the primary tracking technology. We present first efficiency and reconstruction studies to verify the viability of this design concept, and we explore some aspects of its total cost. We end with a summary of recent progress made on the MATHUSLA test stand, a small-scale demonstrator experiment currently taking data at CERN Point 1, and finish with a short comment on future work.