This is the final report submitted to NASA for a Probe-class concept study of the Farside Array for Radio Science Investigations of the Dark ages and Exoplanets (FARSIDE), a low radio frequency interferometric array on the farside of the Moon. The design study focused on the instrument, a deployment rover, the lander and base station, and delivered an architecture broadly consistent with the requirements for a Probe mission. This notional architecture consists of 128 dipole antennas deployed across a 10 km area by a rover, and tethered to a base station for central processing, power and data transmission to the Lunar Gateway, or an alternative relay satellite. FARSIDE would provide the capability to image the entire sky each minute in 1400 channels spanning frequencies from 150 kHz to 40 MHz, extending down two orders of magnitude below bands accessible to ground-based radio astronomy. The lunar farside can simultaneously provide isolation from terrestrial radio frequency interference, auroral kilometric radiation, and plasma noise from the solar wind. This would enable near-continuous monitoring of the nearest stellar systems in the search for the radio signatures of coronal mass ejections and energetic particle events, and would also detect the magnetospheres for the nearest candidate habitable exoplanets. Simultaneously, FARSIDE would be used to characterize similar activity in our own solar system, from the Sun to the outer planets. Through precision calibration via an orbiting beacon, and exquisite foreground characterization, FARSIDE would also measure the Dark Ages global 21-cm signal at redshifts from 50-100. It will also be a pathfinder for a larger 21-cm power spectrum instrument by carefully measuring the foreground with high dynamic range.
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