1 Sets, functions and the real numbers.- 2 Basic properties of real numbers, sequences and continuous functions.- 3 Infinite series.- 4 Uniform convergence.- 5 Functions.- 6. Topics from classical The Gamma-function and the Euler-Maclaurin formula.- 7 Metric spaces.- 8 Fractals and iterated function systems.- 9 Differential calculus on Rm.- Bibliography. Index.