This is an introduction to the fascinating and important interplay between nonlinear dynamics and statistical theories for geophysical flows, designed for a multi-disciplinary audience ranging from beginning graduate students to senior researchers. Novel applications of information theory are utilized to simplify, unify, and compare the equilibrium statistical theories. No previous background in geophysical flows, probability theory, information theory, or equilibrium statistical mechanics is needed to read the text. These topics and related background concepts are all introduced and developed through elementary examples and discussion throughout the text as they arise.