We present the first results from a new redshift survey of southern galaxies. The survey is essentially complete to a magnitude limit of b(J) = 17.15 and consists of 1769 galaxies sampled randomly at a rate of 1 in 20 from the APM galaxy catalogs. Our survey samples a volume approximately 30 times larger than the 14.5 mag CfA Redshift Survey and so can provide an accurate determination of the luminosity function and mean space density of galaxies. After correction for Malmquist bias, the luminosity function is well fitted over the magnitude range -15 > M(bJ) > -22 by a Schechter function with parameters M(bJ)* = -19.50 +/- 0.13, alpha = -0.97 +/- 0.15, and phi* = (1.40 +/- 0.17) x 10(-2) MpC-3 for H0 = 100 kms-1 Mpc-1. We estimate the variation of galaxy density with redshift using a maximum-likelihood method. The absence of a large local void in our survey supports our previous conclusion that the galaxy population must evolve rapidly at relatively low redshifts (z approximately 0.1) to explain the observed number counts over the range 16 less than or similar b(J) less than or similar 19.