These notes are a corrected version of the lecture notes which were distributed to participants at a regional conference held at the University of Georgia on June 12-16, 1972. The theme of the lectures was the use of techniques drawn from the theory of Banach algebras to study Toeplitz operators. An attempt was made at unifying diverse results, and point of view and direction were stressed rather than completeness. In particular, many recent results and problems were discussed.