1.Mean-square approximation for stochastic differential equations. 2.Weak approximation for stochastic differential equations. 3.Numerical methods for SDEs with small noise. 4.Stochastic Hamiltonian systems and langevin-type equation. 5.Simulation of space and space-time bounded diffusions. 6.Random walks for linear boundary value problems. 7.Probabilistic approach to numerical solution of the Cauchy problem for nonlinear parabolic equations. 8.Numerical solution of the nonlinear Dirichlet and Neumann problem based on the probabilistic approach. 9.Applications of stochastic numerics to models with stochastic resonance and to Brownian ratchets.