chapter 1 Motivation and Background -- chapter 2 The Multifractal Formalism -- chapter 3 3The Multinomial Measure -- chapter 4 Lattice Based Multifractals -- chapter 5 Point Centred Multifractals -- chapter 6 Multiplicative Cascade Processes -- chapter 7 Interpoint Distances of Order q and Intrinsic Bias -- chapter 8 Estimation of Point Centred Re´nyi Dimensions with q 2 -- chapter 9 Extrinsic Sources of Bias -- chapter 10 Applications of Dimension Estimation -- chapter 11 Earthquake Analyses.