The author gives a short introductory treatment to matroid theory. After reviewing some mathematical prerequisites in Chapter 1, he discusses various possible axiom systems for matroids as well as matroid duality in Chapter 2. Chapters 3 to 6 deal with the connections between matroids and four other areas of mathematics, namely graphs, combinatorial geometries and lattices, transversal theory and combinatorial optimization. In each of these areas, some interesting (but standard) topics are discussed. There are also a fair number of exercises (with solutions). The book can be recommended as a first introduction to matroids and their unifying power for quite a few areas of mathematics. Of course, one cannot expect to find an in-depth treatment in such a brief text; for this, the classical books recommended by the author have to be consulted.