Includes bibliographical references and index.

1 Magnetism and topology Andre' Thiaville, Jacques Miltat, and Stanislas Rohart 2 Materials for skyrmionics Kai Litzius and Mathias Klaui 3 Characterizing magnetic skyrmions at their fundamental length and time scales Peter Fischer and Sujoy Roy 4 Mapping the magnetic field of skyrmions and spin spirals by scanning probe microscopy Hans J. Hug 5 Scanning probe microscopy methods for imaging skyrmions and spin spirals with atomic resolution Hans J. Hug 6 Static properties of magnetic skyrmions Roberto Zivieri and Oksana Chubykalo-Fesenko 7 Dynamics of magnetic skyrmions Riccardo Tomasello, Luis Sanchez-Tejerina, and Mario Carpentieri 8 Electrical nucleation and detection of magnetic skyrmions Felix Buttner and William Legrand 9 Topological Hall effect Igor Rozhansky and Konstantin Denisov 10 Skyrmions in ferrimagnets Xichao Zhang, Yan Zhou, and Seonghoon Woo 11 Skyrmions in antiferromagnets Oleg A. Tretiakov 12 Multiple skyrmionic states and oblique spirals in bulk cubic helimagnets Andrey O. Leonov and Catherine Pappas 13 Conventional applications of skyrmions Xichao Zhang, Jing Xia, Laichuan Shen, Motohiko Ezawa, Xiaoxi Liu, and Yan Zhou 14 Unconventional applications of skyrmions Wang Kang, Sai Li, Xing Chen, Daoqian Zhu, Xueying Zhang, Na Lei, and Weisheng Zhao 15 Introduction to topology Gabriele Bonanno and Giuseppina D'Agui`