Nuclear quadrupole resonance is a recently developed branch of radio-frequency spectroscopy which is concerned with magnetic resonance absorption in crystals. This absorption is due to reorientation of the nonspherical atomic nuclei against crystalline electric fields. Related phenomena in isolated molecules are briefly mentioned in the Introduction A. This is followed in Sec. B by an elementary treatment of the electrostatic interaction of a nonspherical nucleus with an axially symmetric inhomogeneous electric field as is found approximately in crystallineCl2, a crystal whose structural units are very nearly undisturbedCl2molecules. Electrostatic torques are shown to exist which cause a precession of the nuclear angular momenta around the molecular axes. As this motion is accompanied by a precession of the magnetic and electric moments of the nuclei, which may interact with alternating electromagnetic fields, this leads over to the transition mechanism between the energy levels which are obtained from the corresponding Hamiltonian. Transition and power absorption phenomena are discussed in more detail in Sec. C. In Sec. D effects are treated which either lead to a broadening of the absorption lines or are connected with the thermal agitation in the crystalline lattice. Some experimental aspects are described and examples of observed absorption lines are given in Sec. E. In the concluding Sec. F all nuclei so far investigated with this method are reviewed in three tables. The nuclear information obtainable from such experiments is pointed out.