Since its establishment in 1976, PME (The International Group for the Psychology of Mathematics Education) is serving as a much sought after venue for scientific debate among those at the cutting edge of the field, as well as an engine for the development of research in Mathematics education. A wide range of research activities conducted over the last ten years by PME members and their colleagues are documented and critically reviewed in this handbook, released to celebrate the Group’s 40 year anniversary milestone. The book is divided into four main sections: Cognitive aspects of learning and teaching content areas; Cognitive aspects of learning and teaching transverse areas; Social aspects of learning and teaching Mathematics; and Professional aspects of teaching Mathematics. The selection for each chapter of a team of at least two authors, mostly located in different parts of the world, ensured effective coverage of each field. High quality was further enhanced by the scrupulous review of early chapter drafts by two leaders in the relevant field. The resulting volume with its compilation of the most relevant aspects of research in the field, and its emphasis on trends and future developments, will be a rich and welcome resource for both mature and emerging researchers in Mathematics education.