The cosmic microwave background radiation provides unique constraints on cosmological models. In this Letter we present a summary of the spatial properties of the cosmic microwave background radiation based on the full 4 years of COBE DMR observations, as detailed in a set of companion Letters. The anisotropy is consistent with a scale-invariant power law model and Gaussian statistics. With full use of the multi-frequency 4-year DMR data, including our estimate of the effects of Galactic emission, we find a power-law spectral index of n = 1.2 ± 0.3 and a quadrupole normalization Q rms−P S = 15.3 +3.8 −2.8 µK. For n = 1 the best-fit normalization is Q rms−P S | n=1 = 18 ± 1.6 µK. These values are consistent with both our previous 1-year and 2-year results. The results include use of the ℓ = 2 quadrupole term; exclusion of this term gives consistent results, but with larger uncertainties. The 4-year sky maps, presented in this Letter, portray an accurate overall visual impression of the anisotropy since the signal-to-noise ratio is ∼ 2 per 10 • sky map patch. The improved signal-to-noise ratio of the 4-year maps also allows for improvements in Galactic modeling and limits on non-Gaussian statistics.Subject headings: cosmic microwave background -cosmology: observations 1 NASA/GSFC is responsible for the design, development, and operations of the COBE. Scientific guidance is provided by the COBE Science Working Group. GSFC is also responsible for the development of the analysis software and the delivery of the mission data sets.