History of describing natural objects by geometry is as old as the history of science itself. However, until 1975 it only involved Euclidean objects which restricted the boundary of our imagination to lines, squares, parallelograms, sphere, cube etc. whose dimensions are strictly integer value. In nature there are objects that cannot be described by Euclidean geometry such as the coastline or seashore, river basins, nerve distributions in retina, cloud distribution in the sky, branches of leafless trees etc. are just a few to name. In 1975, B. Mandelbrot conceived the idea of fractals to describe such objects which sometimes appears as stringy or ramified, sometimes appears as wildly folded, sometimes appears fragmented and seemingly irregular and disordered. Soon after its discovery, it became one of the most powerful tools that has been used useful in almost every branches of education.

Most books on fractals, focus on deterministic fractals as the impact of incorporating randomness and time is almost absent. Further, most review fractals without explaining what scaling and self-similarity means. This book introduces the idea of scaling, self-similarity, scale-invariance and their role in the dimensional analysis. For the first time, fractals emphasizing mostly on stochastic fractal, and multifractals which evolves with time instead of scale-free self-similarity, are discussed. Moreover, it looks at power laws and dynamic scaling laws in some detail and provides an overview of modern statistical tools for calculating fractal dimension and multifractal spectrum.