Mandelbrot cascades and related topics -- Law of pure types and some exotic spectra of fractal spectral measures -- The role of transfer operators and shifts in the study of fractals: encoding-models, analysis and geometry, commutative and non-commutative -- Generalized energy inequalities and higher multifractal moments -- Some Aspects of Multifractal analysis -- Heat kernels on metric measure spaces -- Stochastic completeness of jump processes on metric measure spaces -- Self similar sets, entropy and additive combinatorics -- Quasisymmetric modification of metrics on self-similar sets -- Recent progress on dimensions of projections -- The geometry of fractal percolation -- Self-affine sets and the continuity of subadditive pressure -- Stability properties of fractal curvatures.

This volume collects thirteen expository or survey articles on topics including Fractal Geometry, Analysis of Fractals, Multifractal Analysis, Ergodic Theory and Dynamical Systems, Probability and Stochastic Analysis, written by the leading experts in their respective fields. The articles are based on papers presented at the International Conference on Advances on Fractals and Related Topics, held on December 10-14, 2012 at the Chinese University of Hong Kong. The volume offers insights into a number of exciting, cutting-edge developments in the area of fractals, which has close ties to and applications in other areas such as analysis, geometry, number theory, probability and mathematical physics.   .