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Alasgarov was born on September 20, 1928 in Ganja, Azerbaijan. He graduated from Law Department of the Azerbaijan State University. From 1954, he was the Senior Professor and then Dean of the Law Department of Azerbaijan State University, from 1957 he was the Dean of International Law Department. From 1965, he was the Director of the Department of Constitutional Law at the same university. In 1993–1996, he was the Rector of Baku State University. Alasgarov was also an Honorary Doctor of the Kiev State University.