  The APM Galaxy Survey maps the angular positions of more than one million
galaxies to $b_{J} = 20$, covering a volume comparable to the forthcoming Sloan
Digital Sky Survey. A numerical algorithm has been developed to estimate the
power spectrum in three dimensions, using the angular clustering and a model
for the redshift distribution of APM Galaxies. The power spectrum obtained is
free from distortions of the pattern of clustering caused by the peculiar
motions of galaxies. We discuss the uncertainties in the estimated power
spectrum and describe tests of the algorithm using large numerical simulations.
The APM Galaxy power spectrum shows an inflection at a wavenumber $k \sim 0.15
h/Mpc$, with evidence for a peak or turnover in the range $ k \sim 0.03-0.06
h/Mpc$. These features can place strong constraints on Cold Dark Matter models
for structure formation.
