To the outsider, the idea of “noncommutative geometry” is admittedly confusing. Commutativity is an algebraic property, so what about geometry makes it commutative (or not)? No, it doesn’t concern whether Sphere x Torus = Torus x Sphere. What it does concern is the algebras of (continuous, smooth, L^\infty, etc.) functions, which commute under pointwise multiplication. These algebras (along with certain operators) determine the (topological, smooth, Riemannian, spin, measure theoretic, etc.) structure on the manifold. This allows us to recover the geometric structure in algebraic language. Remove the commutativity requirement from those algebraic objects and you arrive at noncommutative geometry. These tools shed light on and can prove results in the classic arena, but they also give a way to understand the structures of many noncommutative spaces that arise, for example, as quotients of ordinary spaces, leaf spaces of foliations, dynamical systems, quantum groups, groupoids, and many examples from physics. In this talk, we introduce the primary objects at play and tools at hand in Connes’ program for noncommutative geometry and equip ourselves to journey away from the familiar and into the land of that which does not commute.