Techniques of dimension calculation in fractal geometry

This master thesis consists of three chapters. In the first chapter, basic concepts related to set, topology, metric and measurement topics are given for better understanding of the following chapters. In the second chapter, the concept of dimension is examined under two headings as topological dimension and fractal dimension. Topological dimension; the small inductive dimension, the large inductive dimension and the cover dimension, the fractal dimension is defined as the dimension of self-similarity, the box counting dimension and the Hausdorff dimension, and the relations between these definitions are given and the results are given. In the third chapter, methods that can find the dimension by calculating from different paths are examined in cases where fractal dimension can not be directly calculated.