Algorithmic music appears to be at a turning point in its history, with many new systems and communities of practice developing together, as vibrant musical culture. This handbook brings together dozens of leading researchers and practitioners in the field, blending technical, artistic, cultural and scientific viewpoints into a whole that considers the making of algorithmic music as a rich, and essentially human activity. The book is organised into four sections, the first grounding the topic in the history, philosophy and psychology of algorithmic music. The second section asks 'what can algorithms in music do?', finding answers in computer science, mathematics, machine learning, bio-inspired computation, manipulation of pattern, computational creativity, and live coding. The third section focuses on the music maker, and the role of algorithms in supporting network music, sonification, music interface design, music in computer games, and spatialisation. The final section opens out to culture at large, and considers algorithmic music in terms of its audience reception, sociology, education, politics and the potential for mass consumption. Perhaps just as importantly, these sections are interleaved with reflective pieces from leading practitioners in the field, allowing us to to grasp the pragmatics of making music with algorithms. Combined, these diverse standpoints provide an absorbing, authoritative survey of research and practice from across the algorithmic music field.