The need to address university mathematics students’ learning needs has become increasingly shared by university mathematics teachers, and beyond, by educational institutions around the world. Indeed, mathematics is both a condition and an obstacle to success for students in many educational programmes vital to the 21st Century knowledge society, for example in pure and applied mathematics, engineering, natural sciences, technology, economics, finance, management and so on. This breadth of impact informs the urgency of developing research on university mathematics education, and of sharing results of this research widely. This book provides a bespoke opportunity for an international audience of researchers in didactics of mathematics, mathematicians and any teacher or researcher with an interest in this area to be informed about state of the art developments and future research agendas. This book emerged from the activities of the research project INDRUM (International Network for Didactic Research in University Mathematics), which aims to contribute to the development of research in didactics of mathematics at all levels of tertiary education, with a particular concern for the development of early-career researchers and for dialogue with university mathematicians. The aim of the book is to provide a deep synthesis of the research field. It is an original contribution which highlights key research perspectives, addresses seminal theoretical and methodological issues and reports substantial results concerning the teaching and learning of mathematics at university level, including the teaching and learning of specific topics in advanced mathematics across a wide range of university programmes.