The great advantage of the Goldhorn script lies in its uncompromising focus on the essentials. The selection of material covers a wide range of mathematical concepts and methods that are relevant to today's physics. In return, the tendency of many lecturers and authors to dwell on supposedly enlightening details is avoided wherever they have proven to be not truly illuminating in practice. In this regard, the script has been continuously optimized over many years of teaching experience. The extensive collection of exercises naturally provides several details that might be missed in the lecture. The arrangement of the material follows not so much a mathematical systematics as the curricular needs of physics studies, which may often seem somewhat unconventional.