Systems of linear equations, matrices and vector spaces are the core topics in this course. Vector spaces consist of vectors (just think of arrows with a certain direction and a certain length, arrows that can be added and multiplied by scalars - that's the algebra!). We introduce vector spaces in an abstract setting so that the corresponding theory can be applied and used in various settings as you will see in other (mathematics) courses ranging from vector analysis to probability theory to optimization. Linear algebra is indispensable for all branches of mathematics, but also for many of the engineering sciences. Since this course is primarily aimed at mathematics students, we specifically pay attention to the way linear algebra is mathematicall structured, and that includes attention for precise mathematical statements and proofs. It is advised to take both Linear Algebra 1 and 2WF30 Linear Algebra 2 (focussing on linear maps between vector spaces like reflections and rotations), since together they cover the standard topics in linear algebra. In Linear Algebra 1 we also discuss complex numbers, which are interesting in themselves, but are especially of use in the techniques of Linear Algebra 2.