The table of precise one‐electron atomic energy levels given by Garcia and Mack in 1965 is expanded to include all atomic numbers and more energy levels, updated by using more recent values of fundamental constants and radiative corrections, and extended to the maximum precision allowed by quantum electrodynamics(QED) calculations. All levels with n?11 are given for Z?15, with n?5 for Z?39, and with n?3 for Z?105. In addition, the S 1/2 and P 1/2 and j?n−1/2 levels with n?20 are given for Z?15, and with n?13 for Z?39. The uncertainty in the QED calculations is given for each level, and the level is given to that precision. Conversions to different units and corrections for changing the Rydberg or nuclear mass values are pointed out. The paper includes a comprehensive listing and brief discussions of all effects considered and of the uncertainties for the calculated and neglected terms. The Fine Structure Interval (difference between the j=l±1/2 levels for given n and l) and its reduced mass and QED contributions are discussed in detail. All known measurements of Lamb shifts and other fine structure differences are compared with calculated values.