Alihuseyn Quliyev was born on 10 June 1929. In 1947, he entered  Baku State University, Faculty of Chemistry. As a fourth-year student he was dispatched to Nızhny Novgorod State University. After completing his higher education in 1952, he worked as a chemical engineer in the city of Tomsk. In 1954, he was a laboratory assistant at the Department of Analytical Chemistry, BSU. From 1954 to 1957, he did postgraduate studies at the Institute of Physics and Mathematics, ANAS. In 1958-1959, he served as a senior research fellow and from 1959 to 1968 headed the laboratory of physical and chemical research of semiconductors. In 1958, Alihuseyn Quliyev defended a PhD thesis, obtaining a ScD degree in 1963. In 1964, he was made a professor of physical chemistry.

In 1968, he was elected a professor at the Department of Physics and Colloidal Chemistry, and became its chair in 1983. He founded a research laboratory of semiconductor materials at BSU.

Alihuseyn Quliyev was one of the outstanding scientists who launched new areas and a research school in the field of physical chemistry. His research interests included the production and purification of semiconductor crystals, new semiconductor phases and their qualities. Alihuseyn Quliyev supervised researches that resulted in the discovery of 70 new semiconductor compounds of thallium-chalcogens. His researches into thermodynamics of semiconductor material allowed to define optimal technological regimes for producing monocrystals. He proposed interpolation equation for analytical expression of generalized and thermodynamic qualities of triple systems. He published 300 papers in CIS and foreign periodicals. Alihuseyn Quliyev supervised three ScD and 24 PhD students to completion.