Budai came from a noble Hungarian family. Already his uncle Ferenc Budai (1760-1802) had been reformed pastor and also the author of a scientific historical lexicon of Polgári Lexicon, which was published posthumously by his nephew. Ézsaiás Budai studied at the Reformed College, the forerunner of the University of Debrecen, and there was Supplent ( teaching assistant ) for Greek and Roman literature. The college funded him, whose father had died early, a two-year study at the University of Göttingen. From 1792 to 1794 he attended lectures by Christian Gottlob Heyne, Christoph Meiners, August Ludwig von Ludwig Timotheus Spittler Schlozer and with whom he remained in friendly correspondence contact for a long time. After a trip to Holland and England, he became a professor of philosophy at the University of Göttingen for a short time, but returned to the 1794 College of Debrecen back. He taught there until 1808 classical literature and history, and then to 1821 religious studies. He reorganized the training at the college by keeping separate educational lectures for the teachers that made renew teaching materials up to date and the library arranged. In the Reformed Church in Hungary in 1813, he became a head notary of the ecclesiastical parish beyond the river Tisza, then in 1821 the first preacher in Debrecen in 1822 and finally superintendent of the parish church beyond the river Tisza. Budai 1831 was made an honorary member of the Hungarian Academy of Sciences.
- Commentatio de causis culturae tardius aquilonares ad quam ad australes Europae regiones propagatae (Göttingen 1794)
- God. Hasse Liber de causis stylized latini (Debrecen 1799)
- Közönséges historia (Debrecen 1800) = " General History "
- Régi Tudos világ historiája (Debrecen 1802) = "History of ancient scholarly world "
- Deák nyelv kezdete példákban (Debrecen 1804) = "Introduction to the Latin language in examples "
- Ratio Institutiones (Debrecen 1807)
- Magyaroszág historiájav (Debrecen 1807) = " History of Hungary "
- Régi Római v. Deak IROK elete (Debrecen 1814 ) = " life of the ancient Roman or Latin writers "
- Propaedeumata Theologiae Christ ( Debrecen 1817)
- Christian. Cellarii latinitatis probatae et exercitae liber memorialis. Cum interpretatione relationship. etc (Debrecen 1831)