Analysis I

This textbook is the first volume of a three-part introduction to analysis. It is characterised by a modern and clear structure that tries to focus on the essentials. Unlike the usual textbooks, no artificial separation is made between the theory of one variable and that of several variables. The reader should be trained in recognising the essential contents and ideas of analysis and acquire a solid foundation for the study of deeper theories. The work is aimed at listeners and lecturers of the beginners' lecture of analysis. With numerous examples, exercises and supplements to the usual lecture material, the text is also suitable for self-study, as a template for in-depth seminars and as a basis for the entire study of mathematics or physics.