If we allow for some randomness in some of the coefficients of a partial differential equation we often obtain a more realistic mathematical model of the situation where is called the two-dimensional stochastic differential equation or in more complicated cases, two-dimensional stochastic integral equation. Some situations where such equations appear and can be used are: Population dynamics, protein kinetics, genetics, experimental psychology, neuronal activity, option pricing, turbulent diffusion, radio-astronomy, helicopter rotor, satellite orbit stability, biological waste treatment, hydrology, indoor air quality, seismology, structural mechanics, fatigue cracking, blood clotting dynamics, cellular energetics, Josephson junctions, communications, stochastic annealing, filtering problems, optimal portfolio problem and mathematical finance. Engineers, physicists and others with a more technical background in mathematical methods who are interested in implementing efficient numerical schemes or developing new schemes for specific classes of applications, can use this book.