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. This subject area is indispensable for most branches of mathematics, and even for many of the engineering sciences. Since this course is primarily aimed at mathematics students, we specifically pay attention to the mathematical structure, and that includes `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.