This book is dedicated to the memory of the Nobel laureate and the great theoretical physicist Lev Davidovich Landau (1908-1968) on the occasion of his centenary. This book brings together fifteen papers contributed by authors from different countries: China, India, Italy, Germany, Mexico, Russia, and USA, covering several core aspects of modern development of Landau legacy and achievements, ranging from Landau's bibliography and life to recent rigorous research on theoretical physics. In his paper entitled "Lev Landau, the Genius that Challenged Stalin", Toscano discusses Landau's life, his influence on theoretical physics in the Soviet Union, and his challenge to Stalin. Kholodenko discusses extensively the impact of the Landau's last paper on physics and mathematics in the new millennium based on Golubeva's famous paper. In his esteemed paper, Sachs presents the philosophical problems of cosmology and time. In their seminal papers, Brandt, Esposito, Salesi, Ma, Wang, and Kleinert review different aspects of Ginzburg-Landau theory, phase transitions, and superconductors. In their remarkable paper on Landau-Lifshits equation, Parga and Gallardo address the importance of this equation and its applications to classical charge particles. Azam, Basu, Dhar, and Li discuss extensively the Landau singularity in QED, Landau quantisation, and non-commutative Landau problem, and other related topics. Rasetti and Raffa report on the multiboson Logical operators, Laughlin states, and Virasoro algebra. Chakraborty in his paper shows the influence of Landau approach to the theory of fluid dynamics.