The Large Observatory for X-ray Timing, LOFT, is designed to perform fast X-ray timing and spectroscopy with uniquely large throughput (Feroci et al. 2014). LOFT focuses on two fundamental questions of ESA's Cosmic Vision Theme "Matter under extreme conditions": what is the equation of state of ultradense matter in neutron stars? Does matter orbiting close to the event horizon follow the predictions of general relativity? These goals are elaborated in the mission Yellow Book (http://sci.esa.int/loft/ 53447-loft-yellow-book/) describing the LOFT mission as proposed in M3, which closely resembles the LOFT mission now being proposed for M4.The extensive assessment study of LOFT as ESA's M3 mission candidate demonstrates the high level of maturity and the technical feasibility of the mission, as well as the scientific importance of its unique core science goals. For this reason, the LOFT development has been continued, aiming at the new M4 launch opportunity, for which the M3 science goals have been confirmed. The unprecedentedly large effective area, large grasp, and spectroscopic capabilities of LOFT's instruments make the mission capable of state-of-the-art science not only for its core science case, but also for many other open questions in astrophysics.LOFT's primary instrument is the Large Area Detector (LAD), a 8.5 m 2 instrument operating in the 2-30 keV energy range, which will revolutionise studies of Galactic and extragalactic X-ray sources down to their fundamental time scales. The mission also features a Wide Field Monitor (WFM), which in the 2-50 keV range simultaneously observes more than a third of the sky at any time, detecting objects down to mCrab fluxes and providing data with excellent timing and spectral resolution. Additionally, the mission is equipped with an on-board alert system for the detection and rapid broadcasting to the ground of celestial bright and fast outbursts of X-rays (particularly, Gamma-ray Bursts).This paper is one of twelve White Papers that illustrate the unique potential of LOFT as an X-ray observatory in a variety of astrophysical fields in addition to the core science.

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