This open access book describes from fundamentals to the state-of-the-art of long-period stacking/order structured Mg alloys, termed LPSO-structured Mg alloys, which have been the subject of research promoted by the Editors-in-Chief Kawamura and Abe since the early 2000s. LPSO-Mg alloys represent unique nanometer-scale layer structures and provide unexpected high strength through kink deformations, which are novel and striking phenomena that have never been seen in any other alloys. The contents of this book cover a wide range of topics of this novel high-strength Mg alloy including alloy design guidelines, atomic-scale structure, kink deformations and disclinations, static/dynamical processing, computer simulations of mechanics, and fatigue and fracture properties. This book provides a platform for those working in lightweight structural materials to spark ideas which encourage extending the LPSO concept to various materials including aluminum and titanium alloys. This book appeals to graduate students learning materials science and modern metallurgy researchers/engineers wishing to develop new light alloys, as well as for general material specialists who have interests on a structure-property relationship. Parts of this book's translation from its Japanese original manuscript were completed with the assistance of artificial intelligence. The author subsequently revised the content.