  The FAST Ultra-Deep Survey (FUDS) is a blind survey that aims for the direct
detection of HI in galaxies at redshifts $z<0.42$. The survey uses the
multibeam receiver on the Five Hundred Meter Aperture Spherical Telescope
(FAST) to map six regions, each of size 0.72 deg$^2$ at high sensitivity ($\sim
50 \mu$Jy) and high frequency resolution (23 kHz). The survey will enable
studies of the evolution of galaxies and their HI content with an eventual
sample size of $\sim 1000$. We present the science goals, observing strategy,
the effects of radio frequency interference (RFI) at the FAST site, our
mitigation strategies and the methods for calibration, data reduction and
imaging as applied to initial data. The observations and reductions for the
first field, FUDS0, are completed, with around 128 HI galaxies detected in a
preliminary analysis. Example spectra are given in this paper, including a
comparison with data from the overlapping GAL2577 field of Arecibo Ultra-Deep
Survey (AUDS).
