We report the initial results of one year of continuous observations of the Sun‘s internal structure from the Michelson Doppler Imager (MDI) on board SOHO. The results have been obtained by inverting frequencies of p and f modes determined with two different methods of averaging over split multiplets. Small systematic differences between the two frequency sets depend primarily on mode frequencies, and, thus, did not significantly affect the inversions. A preliminary study of the systematic effects resulting from asymmetry of oscillation power peaks has also shown no significant influence on the inversion results. The inferred sound-speed profile is in general agreement with the previous data from MDI and ground-based networks. In the energy-generating core, the resolution is substantially improved, and the inversion results indicate a sharp negative perturbation of the sound speed in the core, tending to a positive value near the center. High-precision measurements of the f-mode frequencies have been used to determine the seismic radius of the Sun. The global asphericity estimated from frequency variation across the split mode multiplets has been found to be small, and is consistent with the asphericity during the previous activity minimum. Variations of the solar frequencies during the first year of MDI observations have also been detected.