Son of Albert Vainshtein. In 1953 he defended his doctoral dissertation on the topic "Diffraction of electromagnetic and sound waves at the open end of a waveguide" In 1957 he moved to the Institute of Physical Problems of the Academy of Sciences of the USSR. Professor at MIPT since 1959. Founder of his own scientific school, head of seminars and schools on diffraction and microwave electronics held in the USSR. He made a significant contribution to the formation of the Saratov scientific school of D.I. Trubetskov. Corresponding Member of the Academy ofSciences of the USSR for the Department of General and Applied Physics, specialization "radiophysics and radio engineering" since 1966. Lev Vainshtein's scientific works relate to the theory of diffraction, the theory of open resonators, wave propagation in near-earth space, m-i crowave electronics (he developed a nonlinear theory of a traveling wave lamp), and the theory of signal transmission. The theoretical methods developed by Vainsthein were of great importance for the design of radar systems, microwave technology de- vices, and lasers. The universal function, introduced by him in 1953, through which the solution of anumber of quasi-optics problems isexpressed, was later called the Lev Vainsthein diffraction U (s, p) -function. In the last years of his life he studied the sta- tistics of photocounts, the theory of flicker noise, the theory of cooperative radiation, and the theory of a free electron laser.