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

- Basic theory of truncated Hankel operators

- Difference between truncated Hankel operators and general Hankel operators.

- Recent developments on truncated Hankel operators