Book recommendations for understanding the rigorous mathematical theory of X-ray crystallography include "Mathematical Crystallography" by Harold Hilton, noted as one of the best resources in the field. Other significant texts mentioned are "Mathematical Crystallography: An Introduction to the Mathematical Foundations of Crystallography" by Boisen and Gibbs, and two recommended by MIT: "Crystal Structure Determination" by Werner Massa, which is suitable for beginners, and "Fundamentals of Crystallography" by Carmello Giacarvazzo and others, which is more advanced and assumes prior knowledge. The discussion highlights the importance of both pure and applied mathematics in the study of crystallography.