This chapter first outlines the genesis of the book. We briefly describe the development of university mathematics education as an international field of research and development. This includes the role of the khdm (“Kompetenzzentrum Hochschuldidaktik Mathematik”; Centre for Higher Mathematics Education) and one of its founding directors, Reinhard Hochmuth, to whom this book is dedicated.
We then consider five practice-oriented topics for research in university mathematics education: the secondary-tertiary transition, university students’ mathematical practices, teaching and curriculum design, university students’ mathematical inquiry, and mathematics for non-specialists. These topics represent main areas of recent research and development.
The five topics appear in the book as sections, each with several chapters. The sections and their contents are introduced in the final parts of this first chapter. For each section, we sketch the connection between its chapters and the specific field of research. We further provide a brief description of each chapter in terms of theoretical and methodological approaches, as well as of the results presented.