This book presents the concept of fractal and its geometry with the explanation of how natural objects require different geometry rather than traditional Euclidean geometry and also discusses mathematics of fractals with the simulation results of generated fractal and applications of the fractal geometry in image compression.Image compression is minimizing the size in bytes of a graphics file without degrading the quality of the image to an unacceptable level. The objective of image compression is to reduce irrelevance and redundancy of the image data in order to be able to store or transmit data in an efficient form. Image compression using fractal has a major drawback of large encoding time and several algorithm have been developed to reduce the encoding time for compression. In this thesis various algorithms of Image compression using fractal are presented.