We have measured the =2 Lamb shift in atomic hydrogen. The measurement uses a direct microwave transition between the 2S and 2P states, and employs the new frequency-offset separated-oscillatory-fields (FOSOF) technique. The FOSOF technique is a variation of the Ramsey separated-oscillatory field technique in which the two separated fields have their frequencies slightly offset from each other. Our Lamb shift measurement, along with existing high-precision quantum-electrodynamics theory, leads to a precise measurement of the rms proton charge radius, and therefore helps to resolve the eight-year-old puzzle created by contradictory determinations of the proton size. In particular, this measurement is the direct analog of the very precise 2S-2P muonic-hydrogen determination of the proton size. Our recent work in determining the helium 2P fine structure and our new program to determine the electron electric dipole moment will also be discussed briefly.