<p>Self-dual codes are linear codes whose dual codes are themselves. Algebraic geometry (AG) codes are linear codes defined over algebraic function fields. In this paper, by utilizing the properties of hyperelliptic curves and maximal curves, we construct many new explicit self-dual AG codes and study their parameters. These self-dual AG codes have good properties such as large minimum distance compared with long code length. Especially, in the case of maximal curves, a large number of self-dual AG codes can be obtained. Due to the flexibility of the lengths and large minimum distance, the self-dual AG codes in this paper can be applied in many scenarios of secret sharing schemes, public-key cryptography, coding theory and other related areas.</p>