A survey of two-dimensional electron velocity distributions, ƒ(V), measured near the earth's bow shock using Los Alamos/Garching plasma instrumentation aboard ISEE 2 is presented. This survey provides clues to the mechanisms of electron thermalization within the shock and the relaxation of both the upstream and downstream velocity distributions. First, near the foreshock boundary, fluxes of electrons having a power law shape at high energies backstream from the shock. Although most often they appear as a monotonically decreasing extension of solar wind distributions in the backward hemisphere along the magnetic field direction, , they occasionally appear as a resolved peak in energy. Within the interior of the foreshock, in addition to the hot, isotropic electrons at higher energies, field-aligned depressions in ƒ(V) are observed at the lowest energies (E ≲ 15 eV) and twin angular peaks centered on are observed at intermediate energies (15 eV ≲ E ≲ 45 eV). Such distributions are associated closely with 1-Hz whistler waves. Second, within the shock, cuts through ƒ(V) along ƒ(V∥), often show single maxima offset toward the magnetosheath by speeds comparable to, but larger than, the upstream thermal speed. When sequences of such distributions are observed in a single shock transition, offset speeds increase and peak heights of ƒ(V∥) decrease with increasing penetration toward the downstream (magnetosheath) side. Third, magnetosheath distributions generally have flat tops out to an energy, E0, with maxima substantially lower than that in the solar wind. Occasionally, cuts through ƒ(V) along show one and sometimes two small peaks at the edge of the flat tops making them appear concave upward. The magnetosheath distributions often have strong angular anisotropies which depend on energy. For energies less than E0, ƒ(V∥) > ƒ(V⊥) at constant E, whereas for E > E0, ƒ(V∥) < ƒ(V⊥). The electron distributions characteristic of these three regions are interpreted as arising from the effects of macroscopic (scale size comparable to or larger than the shock width) electric and magnetic fields and the subsequent effects of microscopic (scale size small in comparison with the shock width) fields. In particular, our results suggest that field-aligned instabilities are likely to be present in the earth's bow shock.