Literature is usually recommended for each lecture.

Here I have compiled a list of literature that is worth taking a look at, but which does not really fit any individual mathematics course.

This list is under construction. The year of first publication is indicated. There are newer editions of some of the books.

• George Pólya: 1. Vom Lösen mathematischer Aufgaben (1966) 2. Mathematik und plausibles Schließen (1969) Highly recommended books on the question of how to 'figure it out', how to tackle mathematical problems and perhaps ultimately find a solution.
• Roger Penrose: The Road to Reality: A Complete Guide to the Laws of the Universe (2005) A remarkable book that contains a lot of maths (from the 1st to the 20th semester and beyond), often explained from unusual perspectives.
• Georg Glaeser and Konrad Polthier: Bilder der Mathematik (2009) Many beautiful pictures from various fields of mathematics. With (mostly too) short explanations and further reading.
• Pierre Basieux: Die Architektur der Mathematik -- Denken in Strukturen (2000) Explanations of many basic concepts that one encounters in the introductory lectures of mathematics studies -- more detailed than is usually possible in these lectures.
• Imre Lakatos: Proofs and Refutations -- The Logic of Mathematical Discoveries (1979) In a Platonic dialogue, the process of mathematical research -- establishing hypotheses, improving them, rejecting them, searching for proofs, etc. -- is presented using relatively simple questions. The process of mathematical research -- formulating hypotheses, improving, rejecting, searching for proofs etc. -- is illustrated by means of relatively simple questions. Profound and entertaining.
• John Stillwell: Mathematics and its History (1989)Pythagoras, polynomials, number theory, infinite series, geometry, topology, group theory, combinatorics, etc.: A look at the most important topics in mathematics and how they are connected and have developed historically. The overview character and the emphasis on the relationships between different 'areas' make it a very useful addition to the course.
• Victor Klee and Stan Wagon: Old and New Unsolved Problems in Number Theory and Plane Geometry (1997)Many beautiful, 'classical' mathematical problems that can be formulated elementarily, but whose solution is usually difficult or still unknown; and which were important for the development of mathematics and should therefore be part of the general knowledge of every mathematician. Explanations of the problems and the known solutions.
• Dmitry Fuchs and Serge Tabachnikov: A Chart of Mathematics -- 30 Lectures on Classical Mechanics (2011)Exciting collection of short essays on topics from many areas of mathematics, presented in a sophisticated yet understandable way for a wide range of readers. For example, a marvellous proof of the unsolvability of the 5th degree equation by radicals, which is understandable with school tools.
• Kevin Houston: How to think mathematically (2012)An introduction to mathematical working techniques for first-year students.
• David Hilbert and Stephan Cohn-Vossen: Anschauliche Geometrie (1932)A strange contradiction pervades the study of mathematics: geometry characterises much of modern mathematical language and thought, and yet geometry usually gets short shrift in undergraduate courses. This classic takes you on a walk through the garden of geometry.