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Kinetic theory of weakly turbulent nonlinear processes in plasma helped form the foundation of modern plasma physics. This book provides a systematic overview of the kinetic theory of weak plasma turbulence from a modern perspective. It covers the fundamentals of weak turbulence theory, including the foundational concepts and the mathematical and technical details. Some key obstacles to space plasma applications are also covered, including the origin of non-thermal charged particle population, and radio burst phenomena from the sun. Treating both collective and discrete particle effects, the book provides a valuable reference for researchers looking to familiarize themselves with plasma weak turbulence theory.