A description is given of the spectroscopic properties of the Nd**3** plus ion in various solid-state laser matrices. The effects which may result in multipole interaction between Nd**3** plus ions are considered. An analysis is made of the origin of the difficulties encountered in the determination of the quantum efficiency of the luminescence from the **4F//3/////2 level of Nd**3** plus in various matrices. It is shown that the current ideas on the relationships governing the dissipation of the excitation energy of the Nd**3** plus ions and the existing measurement methods make it possible to determine the concentration dependences of the quantum efficiency of the luminescence from the **4F//3/////2 level of Nd**3** plus in various matrices. The published data and the authors' own results, reported below, are used in plotting the concentration dependences of the quantum efficiency of the luminescence from the **4F//3/////2 level of Nd**3** plus in a variety of solid-state laser matrices. A method for calculating such dependences for crystals is proposed.