manifolds arise naturally in areas of mathematics varying from topology to geometry to analysis, and are important in applications to many fields outside of math (e.g. physics). in this talk, i'll begin by explaining what a manfiold is. then i'll talk a bit about the classification of manifolds in small dimensions. after that, i'll state the poincar\'e conjecture and explain how it is proved (for $n \geq 6$) using the $h$-cobordism theorem. this talk should be accessible to anyone who can see all the pretty pictures on the board.