Title: The Picard groups for unital inclusions of unital $C^*$-algebras,
Abstract: We shall introduce the notion of the Picard group for an inclusion of
$C^*$-algebras. We shall also study its basic properties and the relation
between the Picard group for an inclusion of $C^*$-algebras and the ordinary
Picard group. Furthermore, we shall give some examples of the Picard groups for
unital inclusions of unital $C^*$-algebras.