The properties of crystals, which make up a large part of solid materials, are closely related to the symmetry of their internal structure. The objective of the crystallography lecture is to provide concepts and mathematical fundamentals of symmetry theory, structure-property relationships, and the basic principles of structure determination. Simple crystal structures will be discussed.

The course presents structure-property relationships in complex materials, such as metallic glasses and other disordered materials, magnetic spin ice, and chemically disordered crystals.

The aim is an overview of the different ordering phenomena that occur in materials: magnetic, electrical, mechanical, structural. Special emphasis is placed on a comprehensive definition of the term "ferroic". Novel forms of order, such as multiferroicity, are of particular interest. Their exploration and the material functionalities derived from these are a central theme in our Department.