We present a systematic analysis of the three-flavor Mikheyev-SmirnovWolfenstein (MSW) oscillation solutions to the solar neutrino problem, in the hypothesis that the two independent neutrino square mass differences, δm 2 and m 2 , are well separated: δm 2 ≪ m 2 . At zeroth order in δm 2 /m 2 , the relevant variables for solar neutrinos are δm 2 and two mixing angles, ω and φ. We introduce new graphical representations of the parameter space (δm 2 , ω, φ), that prove useful both to analyze the properties of the electronneutrino survival probability and to present the results of the analysis of solar neutrino data. We make a detailed comparison between the theoretical predictions of the Bahcall-Pinsonneault standard solar model and the current experimental results on solar neutrino rates, and discuss thoroughly the 1 MSW solutions found by spanning the whole three-flavor space (δm 2 , ω, φ).The allowed regions can be radically different from the usual "small mixing"and "large mixing" solutions, characteristic of the usual two-generation MSW approach. We also discuss the link between these results and the independent information on neutrino masses and mixings coming from accelerator and reactor oscillation searches. PACS number(s): 26.65.+t,14.60.Pq,13.15.+g.