In 1983 Dan Voiculescu announced that he had considered the addition problem for non-commutative random variables independent in the sense of free products and proved the corresponding central limit theorem. This was the beginning of free independence. I will introduce free independence in both its analytic and combinatorial presentations. The combinatorial presentation, developed by Nica and Speicher, depends on a calculus of planar diagrams. This is the path to second and higher order independence and also to infinitesimal free independence.