This section discusses recent research on fatigue cracks conducted by leading Japanese researchers, which has often been published only in Japanese. The publication aims to disseminate these findings in English to promote global scientific and technological progress. The research covers three main topics: short fatigue cracks, fatigue crack growth and the threshold, and corrosion fatigue cracks. Key contributions include studies on small crack behavior, threshold behavior, growth and closure of short cracks, and the effects of stress ratio and step loading on fatigue crack growth. The volume provides a comprehensive assessment of stable crack growth research in Japan. Additionally, the section introduces an advanced fracture mechanics textbook that aims to clearly present fundamental aspects of the field to newcomers. The book covers various aspects of fracture mechanics, including linear elastic, dynamic, and elastic-plastic fracture mechanics, as well as models for fiber-reinforced composites and time-dependent fracture. Each chapter is well-illustrated and referenced, making it a highly recommended resource for both beginners and experienced researchers.This section discusses recent research on fatigue cracks conducted by leading Japanese researchers, which has often been published only in Japanese. The publication aims to disseminate these findings in English to promote global scientific and technological progress. The research covers three main topics: short fatigue cracks, fatigue crack growth and the threshold, and corrosion fatigue cracks. Key contributions include studies on small crack behavior, threshold behavior, growth and closure of short cracks, and the effects of stress ratio and step loading on fatigue crack growth. The volume provides a comprehensive assessment of stable crack growth research in Japan. Additionally, the section introduces an advanced fracture mechanics textbook that aims to clearly present fundamental aspects of the field to newcomers. The book covers various aspects of fracture mechanics, including linear elastic, dynamic, and elastic-plastic fracture mechanics, as well as models for fiber-reinforced composites and time-dependent fracture. Each chapter is well-illustrated and referenced, making it a highly recommended resource for both beginners and experienced researchers.