chapter Preliminaries -- chapter Basic Concepts of the Theory of Difference Schemes -- chapter Homogeneous Difference Schemes -- chapter Difference Schemes for Elliptic Equations -- chapter Difference Schemes for Time-Dependent Equations with Constant Coefficients -- chapter Stability Theory of Difference Schemes -- chapter Homogeneous Difference Schemes for Time-Dependent Equations of Mathematical Physics with Variable Coefficients -- chapter Difference Methods for Solving Nonlinear Equations of Mathematical Physics -- chapter Economical Difference Schemes for Multidimensional Problems in Mathematical Physics -- chapter Methods for Solving Grid Equations -- chapter Symbols -- chapter Concluding Remarks.