  In this Letter of Intent (LOI) we propose the construction of MATHUSLA
(MAssive Timing Hodoscope for Ultra-Stable neutraL pArticles), 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 also 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.
