Born into a Jewish family in Botoşani, Graur graduated from the Faculty of Letters of the University of Bucharest and the École Pratique des Hautes Études in Paris (1924–1929). He obtained a Doctor of Philosophy degree from the Sorbonne. After returning to Bucharest, he became involved in academic life and published studies in different periodicals.
Graur founded and was the principal (1941–1944) of the "Liceul particular evreiesc" (Jewish Private High School). In 1946 he started teaching at the university level. In 1955 he was named permanent member of the Romanian Academy. Between 1954 and 1956 he was the Dean of the Faculty of Letters at the University of Bucharest. He wrote many papers and articles on classical philology and etymology. He had many contributions in the field of linguistics, phonetics and grammar of the Latin and Romanian languages.
In 1956, Graur, alongside Dean Iorgu Iordan, leading propagandist Leonte Tismăneanu, and the academics Mihai Novicov, Ion Coteanu, and Radu Florian, he took part in a University inquiry into the anti-communist statements of Paul Goma, a university student who later became a noted dissident and writer; led by Iordan and supervised by the Securitate, the investigation culminated in Goma's expulsion from the Faculty and his subsequent arrest.
- Nom d‘agent et adjectif en roumain, Champion, Paris, 1929
- La romanité du Roumain, Editura Academiei Române, Bucharest, 1965
- The Romance Character of Romanian, Editura Academiei Române, Bucharest, 1965
- Nume de persoane, Bucureşti, Editura Ştiinţifică, Bucharest, 1965
- Tendinţele actuale ale limbii române, Editura Ştiinţifică, Bucharest, 1968
- Scrieri de ieri şi de azi, Editura Ştiinţifică, Bucharest, 1970
- Puţină... aritmetică, Editura Ştiinţifică, Bucharest, 1971
- Nume de locuri, Editura Ştiinţifică, Bucharest, 1972
- Gramatica azi, Editura Academiei Române, Bucharest, 1973
- Mic tratat de ortografie, Editura Ştiinţifică, Bucharest, 1974
- Dicţionar al greşelilor de limbǎ, Editura Academiei Române, Bucharest, 1982
- Puţină gramatică, Editura Academiei Române, Bucharest, 1987
- (Romanian) Mihai Rădulescu, Patimile după Paul Goma
- "CNSAS" (in Romanian). Retrieved June 10, 2014.
- "Lipatti văzut de contemporanii noştri" (in Romanian). Retrieved June 10, 2014.
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