part I An illustrated guide -- chapter 1 Motivating examples -- chapter 2 Selected topics -- chapter 3 Computational and theoretical aspects -- part II Stochastic simulation -- chapter 4 Simulation toolbox -- chapter 5 Monte Carlo integration -- chapter 6 Some illustrations -- part III Discrete time processes -- chapter 7 Markov chains -- chapter 8 Analysis toolbox -- chapter 9 Computational toolbox -- part IV Continuous time processes -- chapter 10 Poisson processes -- chapter 11 Markov chain embeddings -- chapter 12 Jump processes -- chapter 13 Piecewise deterministic processes -- chapter 14 Diffusion processes -- chapter 15 Jump diffusion processes -- chapter 16 Nonlinear jump diffusion processes -- chapter 17 Stochastic analysis toolbox -- chapter 18 Path space measures -- part V Processes on manifolds -- chapter 19 A review of differential geometry -- chapter 20 Stochastic differential calculus on manifolds -- chapter 21 Parametrizations and charts -- chapter 22 Stochastic calculus in chart spaces -- chapter 23 Some analytical aspects -- chapter 24 Some illustrations -- part VI Some application areas -- chapter 25 Simple random walks -- chapter 26 Iterated random functions -- chapter 27 Computational and statistical physics -- chapter 28 Dynamic population models -- chapter 29 Gambling, ranking and control -- chapter 30 Mathematical finance.