© 2015 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society. The Arecibo Ultra-Deep Survey (AUDS) combines the unique sensitivity of the telescope with the wide field of the Arecibo L-band Feed Array (ALFA) to directly detect 21 cm HI emission from galaxies at distances beyond the local Universe bounded by the lower frequency limit of ALFA (z = 0.16). AUDS has collected 700 h of integration time in two fields with a combined area of 1.35 deg2. In this paper, we present data from 60 per cent of the total survey, corresponding to a sensitivity level of 80 μJy. We discuss the data reduction, the search for galaxies, parametrization, optical identification and completeness. We detect 102 galaxies in the mass range of log (MHI/M)-2 log h = 5.6-10.3. We compute the HI mass function (HIMF) at the highest redshifts so far measured. A fit of a Schechter function results in α =-1.37 ± 0.03, ϕ* = (7.72 ± 1.4) × 10-3 h3 Mpc-3 and log (M*HI/M⊙) = (9.75 ± 0.041) + 2 log h. Using the measured HIMF, we find a cosmic HI density of ΩHI = (2.33 ± 0.07) × 10-4 h-1 for the sample (z = 0.065).We discuss further uncertainties arising from cosmic variance. Because of its depth, AUDS is the first survey that can determine parameters for the HIMF in independent redshift bins from a single homogeneous data set. The results indicate little evolution of the comoving mass function and ΩHI within this redshift range. We calculate a weighted average for ΩHI in the range 0HI = (2.63 ± 0.10) × 10-4 h-1.