"This book investigates uncertainty quantification methods for stochastic defects in material microstructure. Pursuing a comprehensive numerical analytical system, the book establishes a fundamental framework for this topic, while emphasizing the importance of stochastic and uncertainty quantification analysis and the significant influence of microstructure defects in the material macro properties. The book is intended for researchers, engineers, and advanced students interested in material defect quantification methods, material reliability assessment, artificial material microstructure optimization, and defect testing"--