Acknowledgements; Introduction: glimpses of the theory beneath Monstrous moonshine; 1. Classical algebra; 2. Modular stuff; 3. Gold and brass: affine algebras and generalisations; 4. Conformal field theory: The physics of Moonshine; 5. Vertex operator algebras; 6. Modular group representations throughout the realm; 7. Monstrous Moonshine; Epilogue; Notation; References; Index.