  This thesis treats two main topics: calibrated symplectic foliations, and
local Lie groupoids. Calibrated symplectic foliations are one possible
generalization of taut foliations of 3-manifolds to higher dimensions. Their
study has been popular in recent years, and we collect several interesting
results. We then show how de Rham's theory of currents, and Sullivan's theory
of structure currents, can be applied in trying to understand the
calibratability of symplectic foliations. Our study of local Lie groupoids
begins with their definition and an exploration of some of their basic
properties. Next, three main results are obtained. The first is the
generalization of a theorem by Mal'cev. The original theorem characterizes the
local Lie groups that are part of a (global) Lie group. We give the
corresponding result for local Lie groupoids. The second result is the
generalization of a theorem by Olver which classifies local Lie groups in terms
of Lie groups. Our generalization classifies, in terms of Lie groupoids, those
local Lie groupoids that have integrable algebroids. The third and final result
demonstrates a relationship between the associativity of a local Lie groupoid,
and the integrability of its algebroid. In a certain sense, the monodromy
groups of a Lie algebroid manifest themselves combinatorially in a local
integration, as a lack of associativity.
