In this article I have tried to give an account of x-ray crystallography as a new subject which is still rapidly expanding. Without any doubt it is an important subject because it is the main method for examining the solid state on an atomic scale. It is an absorbing subject because the fundamental problem of interpreting the experimental evidence still exists and therefore intellectual effort must be put into understanding the scientific principles as well as in deriving results. This effort is at present mainly mathematical, and many people believe that it is probable that the ultimate solution must come through mathematics. But in this article I have endeavoured to show that the subject is essentially a physical one, and have described the physical procedures that I hope will reach the winning post first!