  During commissioning observations, the Sloan Digital Sky Survey (SDSS) has
produced one of the largest existing galaxy redshift samples selected from CCD
images. Using 11,275 galaxies complete to r^* = 17.6 over 140 square degrees,
we compute the luminosity function of galaxies in the r^* band over a range -23
< M < -16 (for h=1). The result is well-described by a Schechter function with
parameters phi_* = 0.0146 +/- 0.0012 h^3 Mpc^{-3}, M_* = -20.83 +/- 0.03, and
alpha = -1.20 +/- 0.03. The implied luminosity density in r^* is j = (2.6 +/-
0.3) x 10^8 h L_sun Mpc^{-3}. The surface brightness selection threshold has a
negligible impact for M < -18. We measure the luminosity function in the u^*,
g^*, i^*, and z^* bands as well; the slope at low luminosities ranges from
alpha=-1.35 to alpha=-1.2. We measure the bivariate distribution of r^*
luminosity with half-light surface brightness, intrinsic color, and morphology.
High surface brightness, red, highly concentrated galaxies are on average more
luminous than low surface brightness, blue, less concentrated galaxies. If we
synthesize results for R-band or b_j-band using the Petrosian magnitudes with
which the SDSS measures galaxy fluxes, we obtain luminosity densities 2.0 times
that found by the Las Campanas Redshift Survey in R and 1.4 times that found by
the Two-degree Field Galaxy Redshift Survey in b_j. We are able to reproduce
the luminosity functions obtained by these surveys if we also mimic their
isophotal limits for defining galaxy magnitudes, which are shallower and more
redshift dependent than the Petrosian magnitudes used by the SDSS. (Abridged)
