We present spectra of the nucleus of M87, taken at the highest spatial resolution available to ground-based observations. Our observations confirm the conclusion of the majority of recent work on this galaxy, that the light from the central point source consists of a flat, probably non-thermal continuum, and a number of strong emission lines characteristic of a LINER. At our spatial resolution we cannot resolve the emission-line region. In the continuum light there are narrow absorption lines of Ca II H and K, quite clearly detected at the redshift of M87 and marginally detected at zero redshift. Thus we detect cool interstellar material in the central regions of M87. It is not possible to measure directly the stellar velocity dispersion in the nucleus of M87, because of contamination by continuum light, emission lines, and interstellar absorption lines. However, the velocity dispersion of the stars between 1 and 2.5 arcsec from the nucleus is 380+/-30 km s-1, and there is no evidence that the dispersion in the stellar component in the nucleus is any higher.