  In this expository article, we introduce the topological ideas and context
central to the Poincare Conjecture. Our account is intended for a general
audience, providing intuitive definitions and spatial intuition whenever
possible. We define surfaces and their natural generalizations, manifolds. We
then discuss the classification of surfaces as it relates to the Poincare and
Thurston Geometrization conjectures. Finally, we survey Perelman's results on
Ricci flows with surgery.
