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This book introduces the fundamentals of probability, statistical, and reliability concepts, the classical methods of uncertainty quantification and analytical reliability analysis, and the state-of-the-art approaches of design optimization under uncertainty (e. g., reliability-based design optimization and robust design optimization). The topics include basic concepts of probability and distributions, uncertainty quantification using probabilistic methods, classical reliability analysis methods, time-variant reliability analysis methods, fundamentals of deterministic design optimization, reliability-based design optimization, robust design optimization, other methods of design optimization under uncertainty, and engineering applications of design optimization under uncertainty.