In the past decade, the field of physics has witnessed renewed advances in physical systems without mirror (parity) symmetry. Experimentally, chiral magnetic skyrmions discovered in real materials have stirred a great deal of interest in future spintronic applications due to their nanoscale size, topological protection, and energy efficiency. Theoretically, the Hall viscosity, a new universal transport coefficient, through the progress in hydrodynamics has triggered extensive theoretical investigation in quantum Hall systems.

This book provides an extensive account of skyrmion dynamics, using various analytical tools, especially the field theory Ward identity that is a first principle method using symmetries and the associated conservation equations. The identity revealed that Hall viscosity is a universal part of skyrmion motion. This book leads readers to frontline research in searching for the role of the mysterious Hall viscosity in skyrmion physics, using the interdisciplinary point of view that encompasses high-energy physics, condensed matter, and materials science. It also provides the necessary backgrounds and physical clarity for advanced undergraduates to meaningfully explore its contents through mathematical expressions conveyed in both vector and index notations.