Analysis in one of the two fundamental courses in mathematics. In the lectures Analysis I - III we treat mathematical induction, convergence, sequences and series, compactness, differentiation and integration, transformation theorems, the implicit function theorem, and more. These are the tools of the trade and no mathematician gets along without them.
The trade is learned by solving the exercises and participating in the exercise groups.
Bröcker, Theodor: Analysis 1, Spektrum der Wissenschaft-Verlag.