Lie groupoids are a category theoretic extension of the concept of a Lie
group and have been the subject of increased interest for differential
geometers in (relatively) recent years.

After discussing their
definition and providing a number of key examples, I plan to describe
some applications of Lie groupoids, including their use as models for
singular spaces (and resulting relation to smooth stacks) and their
relationship with symplectic and Poisson geometry.

I will assume those in the audience have no more than a basic
understanding of category theory and the theory of Lie groups.