The course is based on miscellaneous small chapters, built from examples. The goal is to recall and introduce useful mathematical tools with hands on. The concepts and techniques introduced are useful for other lectures and for future everyday work. We try to treat classical examples as well as some taken from the physics literature. Since we cannot cover all possible subjects, the objective is rather to train and manipulate mathematics, in particular since exact solutions are appealing and indispensable for benchmarking numerical tools.

• Physics and Mathematical Tools: Methods and Examples, A. Alastuey, M. Clusel, M. Magro & P. Pujol, Word Scientific.
• Mathematical Methods for Physicists, T. L. Chow, Cambridge University Press.
• Group Theory in a Nutshell for Physicists, A. Zee, Princeton University Press.