Magnetism and topology

International audience; This chapter explains what topology brings to the physics of magnetic textures in real space, from a physicist's point of view. The statics of magnetic textures is first discussed, and the distinction is made between a topological defect and a topologically stable-or protected-structure, also called topological soliton. The attention is then turned towards the physically observable consequences of topology, mainly in the dynamics of magnetic textures. Connection with experimental observations and applications is made, from early works at the beginnings of magnetic data storage up to the recent work on magnetic skyrmions, which triggered a revival of interest in topology as applied to magnetism.