Seismic data from the four stations of the Apollo passive seismic network have been analyzed to obtain the velocity structure of the moon. The long reverberating train of seismic energy observed in lunar seismograms may be explained by scattering in a near-surface zone. The earliest parts of the seismogram correspond to body wave phases and may be interpreted by conventional methods. There are no clearly identifiable dispersed surface wave trains present on lunar seismograms. This absence can be explained by scattering of surface waves by near-surface heterogeneities. Analysis of body wave phases from artificial impacts of known impact time and position yields a crustal section. In the Mare Cognitum region the crust is about 60 km thick and is layered. In the 20-km-thick upper layer, velocity gradients are high and microcracks may play an important role. The 40-km-thick lower layer has a nearly constant 6.8-km/s velocity. There may be a thin high-velocity layer present beneath the crust. The determination of seismic velocities in the lunar mantle is attempted by using natural impacts and deep moonquakes. The simplest model that can be proposed for the mantle consists of a ‘lithosphere’ overlying an ‘asthenosphere.’ Shear waves are attenuated in the ‘asthenosphere,’ and this zone may be partially molten. No seismic data contradict this model. The best value for the compressional wave velocity of the lithosphere is 8.0 → 8.3 km/s, but this may be an average over several differing regions. Density models are calculated for the moon by using the latest value for the moment of inertia (C/MR² = 0.395±0.005), mean density, and temperature and pressure dependence of density for likely lunar models. The mean density in the lunar mantle, corrected to standard (surface temperature, zero pressure) conditions, is 3.4–3.5 g/cm³. These values together with the mean compressional wave velocities are consistent with an olivine-pyroxene (olivine-rich) lunar mantle but do not exclude other compositions. On the basis of the density models, some limitations can be placed on the maximum allowable radius of an iron-rich lunar core. If the lunar mantle is chemically and mineralogically homogeneous, the maximum radius of such a core is about 700 km for an FeS composition and about 450 km for pure Fe composition. There are no geophysical data that indicate whether the moon does or does not have an iron-rich core.