This project sheds light on trombonist Andy Martin's improvisation and provides tools for further learning. A biographical sketch gives background on Martin, establishing him as a newer jazz master. Through the transcription and analysis of nine improvised solos, Martin's improvisational voice and vocabulary is deciphered and presented as a series of seven thematic hooks. These patterns, rhythms, and gestures are described, analyzed, and presented as examples of how each is used in the solos. The hooks are also set as application exercises for learning jazz style and improvisation. These exercises demonstrate how to use Martin's hooks as a means for furthering one's own improvisation. A full method for successful transcription is also presented, along with the printed transcriptions and their accompanying information sheets.