Пермский государственный университет
Brekhovskikh was born to a peasant family in Strunkino, a small village in Vologda Governorate (now Arkhangelsk Oblast), Russia. He graduated from Perm State University in 1939, from which he received his university degree, and studied under Igor Tamm at the Lebedev Physical Institute (FIAN). There, he received his Candidate of Sciences degree (PhD) in Physics in 1941 for his thesis on X-ray crystallography. After his PhD, he joined FIAN's acoustical laboratories and worked on a naval defence project to develop protection against acoustically triggered mines. He later developed a theory of the propagation of acoustical waves in layered media, for which he received his DSc in Physics and Mathematics from FIAN in 1947.