This book is a comprehensive introduction to fractal geometry, focusing on the mathematical concepts and properties of fractals. It is intended for students with a background in calculus and basic abstract set theory, and it provides a rigorous treatment of the subject. The book begins with an overview of fractal examples, including the Cantor set, Sierpiński gasket, and other self-similar structures. It then moves on to metric topology, covering topics such as metric spaces, compactness, and the Hausdorff metric. The book then explores topological dimension, discussing zero-dimensional spaces, covering dimension, and inductive dimension. It then delves into self-similarity, examining ratio lists, string models, and graph self-similarity. The book then introduces measure theory, including Lebesgue measure, metric outer measure, and measures for strings. The final chapters focus on fractal dimension, discussing Hausdorff measure, packing measure, and other fractal dimensions. The book also includes a variety of examples and exercises, as well as a glossary of terms, an index of notation, and a list of fractal examples. The book is written for students who have a basic understanding of calculus and are interested in learning more about fractal geometry. It is not intended to be a comprehensive overview of all aspects of fractal geometry, but rather a focused introduction to the subject. The book is also accompanied by a variety of illustrations and diagrams, which help to visualize the concepts discussed. The book is written in a clear and accessible style, making it suitable for both undergraduate and graduate students. It is an essential resource for anyone interested in learning more about fractal geometry.This book is a comprehensive introduction to fractal geometry, focusing on the mathematical concepts and properties of fractals. It is intended for students with a background in calculus and basic abstract set theory, and it provides a rigorous treatment of the subject. The book begins with an overview of fractal examples, including the Cantor set, Sierpiński gasket, and other self-similar structures. It then moves on to metric topology, covering topics such as metric spaces, compactness, and the Hausdorff metric. The book then explores topological dimension, discussing zero-dimensional spaces, covering dimension, and inductive dimension. It then delves into self-similarity, examining ratio lists, string models, and graph self-similarity. The book then introduces measure theory, including Lebesgue measure, metric outer measure, and measures for strings. The final chapters focus on fractal dimension, discussing Hausdorff measure, packing measure, and other fractal dimensions. The book also includes a variety of examples and exercises, as well as a glossary of terms, an index of notation, and a list of fractal examples. The book is written for students who have a basic understanding of calculus and are interested in learning more about fractal geometry. It is not intended to be a comprehensive overview of all aspects of fractal geometry, but rather a focused introduction to the subject. The book is also accompanied by a variety of illustrations and diagrams, which help to visualize the concepts discussed. The book is written in a clear and accessible style, making it suitable for both undergraduate and graduate students. It is an essential resource for anyone interested in learning more about fractal geometry.