Fractal geometry has become an influential field of study, deeply impacting numerous areas of mathematics and sciences over recent decades. Rooted in the works of Benoit B. Mandelbrot, fractal geometry explores mathematical structures that exhibit self-similarity at varying scales. Unlike traditional Euclidean geometry, which deals with regular shapes, fractal geometry applies to irregular and complicated patterns found in nature, such as coastlines, mountains, and biological structures. Fractal objects are characterised by intricate, repeated patterns, whether deterministic or statistical in nature numbers. They have gained attention not only for their theoretical depth but also for their practical applications. These include areas like harmonic analysis, probability theory, dynamic systems, computer graphics, and even fields as diverse as physics, biology, and economics. The appeal of fractals extends beyond mathematics, blending artistry with mathematical theory and providing a novel way to represent complicated natural forms. This presentation provides an overview of fractal geometry, distinguishing between self-affine and self-similar structures and discussing their relevance in both theoretical contexts and real-world applications. Special attention will be paid to the role fractals play in fields such as chaos theory, image compression, and dynamic systems modelling.