Research applications of complex systems and nonlinear physics are rapidly expanding across various scientific disciplines. A common theme among them is the concept of “self-organized criticality systems”, which this volume presents in detail for observed astrophysical phenomena, such as solar flares, coronal mass ejections, solar energetic particles, solar wind, stellar flares, magnetospheric events, planetary systems, galactic and black-hole systems. The author explores fundamental questions: Why do power laws, the hallmarks of self-organized criticality, exist? What power law index is predicted for each astrophysical phenomenon? Which size distributions have universality? What can waiting time distributions tell us about random processes? This is the first monograph that tests comprehensively astrophysical observations of self-organized criticality systems for students, post-docs, and researchers. A highlight is a paradigm shift from microscopic concepts, such as the traditional cellular automaton algorithms, to macroscopic concepts formulated in terms of physical scaling laws.