  This thesis is divided into four chapters. The first chapter discusses the
relationship between stacks on a site and groupoids internal to the site. It
includes a rigorous proof of the folklore result that there is an equivalence
between the bicategory of internal groupoids and the bicategory of geometric
stacks. The second chapter discusses standard concepts in the theory of
geometric stacks, including Morita equivalence, stack symmetries, and some
Morita invariants. The third chapter introduces a new site of Dirac structures
and provides a rigorous answer to the question: What is the stack associated to
a symplectic groupoid? The last chapter discusses a remarkable class of Poisson
manifolds, called b-symplectic manifolds, giving a classification of them up to
Morita equivalence and computing their Picard group.
