This research program is for the fabrication and study of the electronic properties of high-quality electron systems in GaAs/AlGaAs heterostructures which are laterally confined with atomic precision. We will make use of a new and promising fabrication technique, namely regrowth by molecular beam epitaxy (MBE) on the edge of an in-situ-cleaved wafer which contains thin-film layers previously grown by MBE. The precision of the lateral structures (on the cleaved surface) in this technique is limited by the initial MBE growth and, therefore, is about the atomic size. This is by far better than what is presently achievable by conventional lithography techniques. We propose to fabricate novel systems such as lateral resonant tunneling structures and lateral superlattices, and study their electronic properties through quantum transport measurements.