This extensive book is concerned with all aspects of curves and their possible dimension notions. It consists of four larger parts including an appendix concerning some analysis, geometric measure theory and convexity. The first two parts contain all which is necessary for a beginner in this kind of theory. For simplicity the author has provided the reader with elementary topology and measure theory based on sets of lines. The second part is then devoted to rectifiable sets, but the level of comprehension is not increased to much. It includes the notions of polygonal curves as well as the technique of Minkowski sausages. The third part describes different techniques to obtain purely fractal curves including all important historical examples. Sometimes the reader wonders why it is necessary to have such a lot of different dimension notions. Unfortunately, the book leaves open the answer except of some artificial examples.