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This is an open access title. It is made available under a Creative Commons Attribution-Non Commercial-No Derivatives 4.0 International licence. It is available to read and download as a PDF version on the Oxford Academic platform. The opportunities for doing scattering experiments at synchrotron and neutron facilities have grown rapidly in recent years and are set to continue to do so into the foreseeable future. This text provides a basic understanding of how these techniques enable the structure and dynamics of materials to be studied at the atomic and molecular level. Although mathematics cannot be avoided in a theoretical discussion, the aim has been to write a book that most scientists will still find approachable. To this end, the first two chapters are devoted to providing a tutorial background in the mathematics and physics that are implicitly assumed in other texts. Thereafter, the philosophy has been one of keeping things as simple as possible.