Music composition using Artificial Intelligence is a well-established area of study with research dating back over six decades. From the time the mathematical model of computation was developed by Alan Turing in the 1940s, the question of whether computers can be built to match human level intelligence has been debated. Creativity is certainly considered to be a sign of intelligence, and many areas of Artificial Intelligence have pursued ways to emulate the creative spark found in humans. Music Composition via Artificial Intelligence falls into this category. This thesis explores the application of Artificial Intelligence approaches towards the goal of composing music by implementing three approaches found in Artificial Intelligence and studying their results.