The philosophy and scope of fractal geometry, Scaling and self similarity, Hausdorff measure and dimensions, Boxcounting dimensions, Techniques for calculating dimensions, Local structure and projections of fractals, The Thermodynamic Formalism: Pressure and Gibb’s measures, the dimension formula, Invariant measuresand the transfer operator, Entropy and the Variational principle; The ergodic theorem; The renewal theorem; Martingales and the convergence theorem, BiLipschitz equivalence of fractals; Multifractal Analysis; Applications of fractals: Iterated function systems (IFS) and Recurrent IFS, Applications to image compression, Julia sets and the Mandelbrot set, Random fractals, Brownian motion and Random walks, Percolation, Fractal interpolation, 
Reference Books:
 Mandelbrot B. Fractal Geometry of Nature, W.H. Freeman and Company
 Barnsley M. F. Fractals Everywhere, Academic Press
 Mattila. Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability, Cambridge University Press
 Peitgen, Jurgens and Saupe, Chaos and Fractals, New Frontiers
