Linear algebra, alongside analysis, is a mandatory subject in the mathematical foundation for all students in technical, natural sciences, and business disciplines at universities and universities of applied sciences. Apart from basic vector calculations and simple linear equation systems, learning linear algebra requires a higher level of abstraction from the very beginning of the studies than what is necessary for analysis. This book addresses this fact particularly by guiding learners to the most important results of linear algebra through simple examples and understandable special cases, while largely avoiding formal mathematical proofs, yet remaining mathematically precise. In other words, this book is written for the application-oriented reader.