Transmission electron microscopes use electrons with wavelengths of a few picometers, potentially capable of imaging individual atoms in solids at a resolution ultimately set by the intrinsic size of an atom. Due to lens aberrations and multiple scattering of electrons in the sample, the image resolution reached is 3 to 10 times worse. By inversely solving the multiple scattering problem and overcoming the electron-probe aberrations using electron ptychography, we demonstrate an instrumental blurring of under 20 picometers and a linear phase response in thick samples. The measured widths of atomic columns are limited by thermal fluctuations of the atoms. The method is also capable of locating embedded atomic dopant atoms in all three dimensions with sub-nanometer precision from only a single projection measurement.