In this series of lectures, we outline the basics of the theory of infinity harmonic functions, also known as (absolutely) minimal Lipschitz extensions. Armstrong will use the first half of each meeting to discuss the existence and uniqueness of infinity harmonic functions as well as connections to tug-of-war games and the infinity calculus of variations. Smart will talk in the second half of both meetings and present the regularity theory, including the recent result of Evans-Smart on the pointwise differentiability of infinity harmonic functions. The parallel presentations will have contrasting points of view, since it is only the regularity theory that seems to require any PDE methods.