Conducting is non-verbal communication of musical ideas through the use of gestures made by the hands, arms, and body, as well as expressions made by the face. It is at once physical, psychological, mental, and potentially even spiritual, requiring presence, an ability to listen, respond, guide, catalyze, shape, lead, sometimes follow, and most of all, invite and inspire musicians. This document addresses gesture as a manifestation of musical sound and how conductors approach these physical, non-verbal motions to affect musical sound and how they might be interpreted by performers. Using anthropologist Ray Birdwhistell's Kinesics in Context, and studies by psychologist Paul Ekman and his colleagues, I relate kinesics and categories of non-verbal communication to conducting and the teaching of gesture, and how this non-verbal language communicates musical intention. Through information gleaned from interviews with preeminent American conducting pedagogues as well as my own experience as a student and teacher of conducting, I present several approaches to teaching conducting aimed at helping developing conductors improve and cultivate their craft. I also offer a compilation and expansion of exercises that encourage conductors to maximize their expressive potential and most effectively communicate with their ensemble. Finally, this document addresses how the standard idea of gesture applies to Gerard Grisey's Partiels from his Espaces Acoustiques and Witold Lutoslawski's Chain 1, taking into account new notational elements. The purpose of this document is to elucidate the gestural language of conducting and the visual aspect of effectively communicated sound, and provide a fresh pedagogical approach to conducting.