This paper describes a new approach to making altimeter measurements from off-nadir radar signal returns and its oceanographic and geophysical applications. The approach is based on the technique of radar interferomety and the new instrument is called the Wide-Swath Ocean Altimeter (WSOA). WSOA is designed to be flown with a Jason class conventional dual-frequency altimeter system, including a multi-frequency radiometer for the correction of the effects of water vapor in the troposphere. WSOA will extend the measurement from a line along the nadir to a swath of 200 kin centered on the nadir track. The most important application of WSOA is to provide the first synoptic maps of the global oceanic eddy field with a spatial resolution of 15 km x 15 km. The strong currents and water property anomalies (in temperature, salinity, oxygen, etc.) associated with ocean eddies are a major factor affecting the oceanic general circulation and the biogeochemical cycles of the ocean. WSOA will also provide measurements that allow the monitoring and study of coastal currents and tides that affect the lives of half of the world's population. The intrinsic resolution of WSOA in the look direction of the interferometric radar is about 1 km, allowing the estimation of sea surface slope with an accuracy of 1 micro radian down to a wavelength of 20 km for a 2-year mission (15 km for a 5-year mission). This capability will make contributions to the mapping of the details of the sea floor topography.