Abstract: Dvoretzky's Theorem states (in one form) that every centrally symmetric convex body contains a cross-section of large dimension that is almost a sphere, a fact that is not immediately apparent (to most people) even for cubes or other bodies with finitely many extreme points.I will discuss a proof of this fact which involves geometry, probability and functional analysis, and I will discuss at least one application of the theorem.Please note that this talk will only contain material that has been known for at least 20 years, and I will start with the basics.