Current methods for producing single-walled carbon nanotubes (SWNTs) lead to heterogeneous samples containing mixtures of metallic and semiconducting species with a variety of lengths and defects. Optical detection at the single nanotube level should thus offer the possibility to examine these heterogeneities provided that both SWNT species are equally well detected. Here, we used photothermal heterodyne detection to record absorption images and spectra of individual SWNTs. Because this photothermal method relies only on light absorption, it readily detects metallic nanotubes as well as the emissive semiconducting species. The first and second optical transitions in individual semiconducting nanotubes have been probed. Comparison between the emission and absorption spectra of the lowest-lying optical transition reveal mainly small Stokes shifts. Side bands in the near-infrared absorption spectra are observed and assigned to exciton-phonon bound states. No such sidebands are detected around the lowest transition of metallic nanotubes.