This book presents the state-of-the-art research on the teaching and learning of linear algebra in the first year of university, in an international perspective. It aims at giving to university teachers in charge of linear algebra courses a wide range of information from works including theoretical and experimental issues. These works try to better understand the meaning of linear algebra in an epistemological approach, as well as the constraints and the difficulties in its teaching and learning. They also present teaching designs with the analysis of their experimentation. However, it would be vain to expect a miraculous way for teaching linear algebra, rather elements of reflection are given to the reader with keys for his or her own experimentation. Through the variety of the works presented, this book also discusses theoretical issues which are consistent for all research in maths education at tertiary level.