This is the third book containing examples from the Theory of Complex Functions. The first topic will be examples of elementary analytic functions, like polynomials, fractional functions, exponential functions and the trigonometric and the hyperbolic functions. Then follow some examples of harmonic functions. Even if I have tried to be careful about this text, it is impossible to avoid errors, in particular in the first edition. It is my hope that the reader will show some understanding of my situation