In this lecture we introduce truncated Toeplitz operators, which has been introduced by Sarason. We focus the basic theory and difference between truncated Toeplitz operators and general Toeplitz operators. Moreover we review the recent developments in the theory of truncated Toeplitz operators.

- Basic theory of truncated Toeplitz operators

- Difference between truncated Toeplitz operators and general Toeplitz operators.

- Recent developments on truncated Toeplitz operators