This book addresses how pre-service mathematics teachers (PMTs) can be better prepared to design and teach lessons that engage students in reasoning and proving (R&P), a core yet persistently challenging aspect of mathematics education. Building on the European MaTeK project, the book presents a multi-phase intervention developed collaboratively by five universities to enhance PMTs’ design capacity in teaching R&P across diverse curricular contexts. Grounded in current international research, the book combines theoretical and empirical perspectives on R&P, lesson design, and teacher design capacity. It analyzes PMTs’ evolving understanding of reasoning, their task and lesson designs, and their reflections on classroom implementation. The findings highlight the transformative potential of international collaboration and structured feedback in preparing teachers for contemporary classrooms. Combining conceptual clarity with practical examples, the book offers valuable insights for mathematics teacher educators, researchers, and curriculum developers. It contributes to ongoing discussions on how to support teachers in creating learning environments where mathematical reasoning and proof are integral to student learning.