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This textbook introduces a new perspective that emphasizes the propagation of randomness in engineering systems and the integration of physical mechanisms into probabilistic structural reliability analysis. It develops a unified theoretical framework that bridges classical mathematical approaches with physically-informed reliability assessment, offering a comprehensive foundation for both researchers and practitioners. It highlights the impact of load processes & material behavior on structural reliability, and covers component-level & global reliability, static & dynamic loads, and advanced reliability-based design optimization. Then, it investigates the probability density evolution method (PDEM) & other physically-based stochastic methods, connecting classical and contemporary reliability theories.