As a complex self-bound quantum many-body system, atomic nuclei exhibit various shapes due to significant long-range multipole-multipole interactions among nucleons. Studies of these shapes and the associated nuclear moments have deepened our understanding of simple patterns in complex nuclear systems and are connected to fundamental questions in particle physics, astrophysics, and beyond. In recent decades, advancements in global facilities and detectors have led to increased attention on the study of reflection asymmetry in atomic nuclei, both experimentally and theoretically.The collection of research and review articles presented in this book offers a detailed account of various sub-topics, including reflection asymmetric shapes, nuclear shape phase transitions, nuclear masses, nuclear fission, clustering structures, high-spin states, octupole collective motions, electric dipole moments, and CP violation. These contributions not only highlight the progress made thus far but also pave the way for future investigations. The book will be particularly useful for researchers in nuclear physics.