This textbook introduces you to the fundamental concepts and methods of linear algebra in an understandable way, building on the content from mathematics classes in secondary education levels I and II. Special emphasis is placed on visualizing the mathematical terms and procedures discussed. Central concepts are developed through examples and then generalized, allowing you to gradually make abstractions from familiar material. You can follow computational procedures in a traditional manner or with the help of a computer. The book enables you to use the free computer algebra system Maxima for topics in linear algebra.