We describe the 2dF Galaxy Redshift Survey (2dFGRS) and the current status of the observations. In this exploratory paper, we apply a principal component analysis to a preliminary sample of 5869 galaxy spectra and use the two most significant components to split the sample into five spectral classes. These classes are defined by considering visual classifications of a subset of the 2dF spectra, and also by comparison with high-quality spectra of local galaxies. We calculate a luminosity function for each of the different classes and find that later-type galaxies have a fainter characteristic magnitude, and a steeper faint-end slope. For the whole sample we find M*=−19.7 (for Ω=1, H0=100 km s−1 Mpc−1), α=−1.3, φ*=0.017. For class 1 (‘early-type’) we find M*=−19.6, α=−0.7, while for class 5 (‘late-type’) we find M*=−19.0, α=−1.7. The derived 2dF luminosity functions agree well with other recent luminosity function estimates.