The self-evolving world modelSelf-evolving world model (SEWM) represents a foundational advancement in artificial intelligence, enabling agents to autonomously refine their internal representations and predictive capabilities through continuous interaction with the environment. This chapter provides a comprehensive framework by formalizing SEWM into four core components: the Model (encompassing perception, task, policy, actor, and reward), Memory, Tools, and the Dynamics Optimizer. Mathematically, the self-evolving world model aims to learn a dynamics function \(P(s_{t+1} | s_t, a_t, M, D, L, P)\) that achieves functional equivalence with the true environment. The self-evolving mechanism is driven by closed-loop optimization via the Dynamics Optimizer. The chapter systematically explores self-evolution within each component (e.g., perception, task, policy, actor, and reward evolution for the Model; Memory; Tools; Dynamics Optimizer) and between components (e.g., joint model-memory, joint model-tools, joint model-optimizer self-evolution). This structured formalism promotes the development of adaptive, robust, and generalizable AI systems capable of lifelong learning.