Crystallography is a subject with one hard conceptual wall and two quite separate destinations. The wall is reciprocal space: the fact that a diffraction pattern is a Fourier transform of the structure, so the thing you measure is not a picture of the crystal but its transform, and the missing phases are the reason structure determination is a craft. Almost everyone who bounces off crystallography bounces off there, and it happens because they met a comprehensive textbook before they had any physical picture of a lattice.
The second issue is that the field forks. Small-molecule and materials crystallography — chemists, metallurgists, mineralogists, powder diffraction — and macromolecular crystallography — proteins, nucleic acids, synchrotrons — use the same theory but different books, different software and different practical problems. Reading the wrong branch is not fatal, but it is a lot of pages you did not need.
Before any mathematics
Start with Crystallography by A. M. Glazer, the Very Short Introduction. It is roughly 150 small pages by a serious crystallographer, and it gives you lattices, symmetry, diffraction and what the field is for, with no equations to speak of. It is a better opening than jumping into an undergraduate text because it supplies the physical picture the textbooks assume.
Crystals and Crystal Structures by Richard J. D. Tilley is the gentle undergraduate follow-up, chemistry-flavoured and strong on real structure types. Then two pieces of history that are worth reading precisely because they are not neutral: Rosalind Franklin: The Dark Lady of DNA by Brenda Maddox is a proper biography of the crystallographer whose data underpinned the double helix, and The double helix is James D. Watson's own 1968 memoir — a primary source, gossipy, self-serving and widely criticised for its treatment of Franklin. Reading the memoir after the biography rather than before it makes the difference obvious.
The core theory
Introduction to crystallography by Donald Sands is a short, cheap classic on symmetry, point groups and space groups. It does the bookkeeping properly and it will not take a fortnight. The Basics of Crystallography and Diffraction by Christopher Hammond is the standard student bridge and the single most useful volume here: it takes you from lattice geometry through the reciprocal lattice and the Ewald sphere carefully, with the vector algebra spelled out. If reciprocal space is the wall, this is the ladder.
Elements of X-ray diffraction by B. D. Cullity is the materials-science classic — powder diffraction, phase identification, stress and texture measurement. It is the practical book for anyone whose samples are metals, ceramics or minerals rather than single crystals grown for the purpose.
Structure determination, by branch
For chemistry and small molecules: Crystal Structure Determination by Werner Massa is the practical bench guide to taking a small-molecule dataset through to a refined structure. Crystal structure analysis by Jenny Pickworth Glusker and Kenneth Trueblood is the compact primer covering the same ground with more explanation and less procedure. Structure Determination by X-ray Crystallography by Mark Ladd and Rex Palmer is the comprehensive textbook with worked problems, and it is where the mathematics becomes unavoidable.
Fundamentals of crystallography, edited by Carmelo Giacovazzo, is the reference work of the field: encyclopaedic, multi-author, and not a book to learn from cold. Symmetry relationships between crystal structures by Ulrich Müller is the specialist end — group-subgroup relations and Bärnighausen trees — and it requires comfort with group theory.
For biology: Crystallography made crystal clear by Gale Rhodes is written for biologists who need to understand a structure they did not solve, and it is unusually honest about resolution, model bias and what a deposited structure does and does not prove. Biomolecular crystallography by Bernhard Rupp is the comprehensive macromolecular textbook — long, current and the standard reference for people running the experiment.
Follow the full sequence and pick your branch at the halfway point rather than at the bookshop.
Follow the full ordered path here: Best Books on Crystallography and X-ray Diffraction, in Order.