The results of analysis of the anomalous magnetic field of the Reykjanes Ridge and the adjacent basins are presented, including a new series of detailed reconstructions for magnetic anomalies 1 - 6 in combination with a summary of the previous geological and geophysical investigations. We furnish evidence for three stages of evolution of the Reykjanes Ridge, each characterized by a special regime of crustal accretion related to the effect of the Iceland hotspot. The time interval of each stage and the causes of the variation in the accretion regime are considered. During the first, Eocene stage (54 - 40 Ma) and the third, Miocene-Holocene stage (24 Ma-present time at the northern Reykjanes Ridge north of 59° N and 17 - 11 Ma-present time at the southern Reykjanes Ridge south of 59° N), the spreading axis of the Reykjanes Ridge resembled the present-day configuration, without segmentation, with oblique orientation relative to the direction of ocean floor opening (at the third stage), and directed toward the hotspot. These attributes are consistent with a model that assumes asthenospheric flow from the hotspot toward the ridge axis. Decompression beneath the spreading axis facilitates this flow. Thus, the crustal accretion during the first and the third stages was markedly affected by interaction of the spreading axis with the hotspot. During the second, late Eocene-Oligocene to early Miocene stage (40-24 Ma at the northern Reykjanes Ridge and 40 to 17-11 Ma at the southern Reykjanes Ridge), the ridge axis was broken by numerous transform fracture zones and nontransform offsets into segments 30-80 km long, which were oriented orthogonal to the direction of ocean floor opening, as is typical of many slow-spreading ridges. The plate-tectonic reconstructions of the oceanic floor accommodating magnetic anomalies of the second stage testify to recurrent rearrangements of the ridge axis geometry related to changing kinematics of the adjacent plates. The obvious contrast in the mode of crustal accretion during the second stage in comparison with the first and the third stages is interpreted as evidence for the decreasing effect of the Iceland hotspot on the Reykjanes Ridge, or the complete cessation of this effect. The detailed geochronology of magnetic anomalies 1-6 (from 20 Ma to present) has allowed us to depict with a high accuracy the isochrons of the oceanic bottom spaced at 1 Ma. The variable effect of the hotspot on the accretion of oceanic crust along the axes of the Reykjanes Ridge and the Kolbeinsey and Mid-Atlantic ridges adjoining the former in the north and the south was estimated from the changing obliquity of spreading. The spreading rate tends to increase with reinforcing of the effect of the Iceland hotspot on the Reykjanes Ridge.