This book extends our understanding of the faulting process of natural earthquakes as a complex system. The complex faulting process is generally described by considering a deterministic source (coherent rupture) and a stochastic source (incoherent ruptures). Long-period and short-period approximations provide the scaling law of deterministic and stochastic source parameters of natural earthquakes in a general manner. New concepts of stochastic scaling and non-linear scaling law are introduced to represent such complex phenomena of earthquake activities at local, regional and global levels. There are found three modes of complex systems derived from stochastic scaling, which characterize the minimum total power (energy) of the system. These systems predict corresponding power spectra of l/f, Kolmogorov and Lorentz types. Since the stochastic scaling is general, the theory can also be applied to the physics of complex systems in nature. Audience: Graduate and undergraduate students in geophysics and geology, and seismologists, civil engineers, geophysicists and geologists.