  In a previous paper we generalized the theory of W*-modules to the setting of
modules over nonselfadjoint dual operator algebras, obtaining the class of
weak*-rigged modules. At that time we promised a forthcoming paper devoted to
other aspects of the theory. We fulfill this promise in the present work and
its sequel "Rigged modules II", giving many new results about weak*-rigged
modules and their tensor products. We also discuss the Picard group of weak*
closed subalgebras of a commutative algebra. For example, we compute the weak
Picard group of $H^{\infty}(D)$, and prove that for a weak* closed function
algebra A, the weak Picard group of A is a semidirect product of the
automorphism group of A, and the subgroup consisting of symmetric equivalence
bimodules.
