This study presents an analysis of a detailed topographic survey with a multi-beam bathymetric survey system, of the crest and upper flank of the Galapagos Rift between 85¿20' and 86¿17'W. The morphology of this region is distinctly lineated due to elongate ridges and troughs parallel to the ridge axis (first order relief). These ridges and troughs are called lineaments, and occur in pairs of strikingly similar appearance on both sides of the axis. Each lineament exhibits a second order relief consisting of highs and lows that alternate along the strike of the lineament. A high in one of a pair of lineaments is opposed to a low in the other. Finally, a third order relief of small, rounded hills is a result of volcanic construction in constrast to the first and second order relief which are of structural origin. The evolution of the rise primarily due to processes operating within 5 km to either side of the axis. In this zone, lineaments form by progressive faulting over a long period of time. Two paired lineaments start to form at slightly different times. This is related to the instantaneous position of the primary zone of extrusion, which migrates continuously across the rift valley floor. The process of formation of the lineaments is completed in the crestal ranges: beyond, the pattern is frozen and the lineaments are transferred downslope with only subsidence and relief reduction by faulting. The constant width of the lineaments probably reflects the depth near the axis of a transition from brittle to ductile crust at approximately 1 km. The extreme symmetry of the lineaments across the axis remains unexplained. The antisymmetric high-low second order relief is attributed to shallow intrusions. It is not clear why the pattern is so regular. Comparison with the Famous area at the Mid-Atlantic ridge suggests a relation between the height of the rift walls, the depth of the rift valley floor, the relative amount of structural extension and the ease with which the magma can reach the surface from the source. The magma source in the Famous area may be relatively deep so that the only surface access is by localized, diapric upwelling. This is reflected in the short ridge segments and short, closely spaced transform faults of that region. In contrast, the magma source in the Galapagos area seems to be much shallower so that magma is available everywhere along the rise axis. Here, ridge segments are long, and only major transforms occurs.