Approximate Block Method for Solving the Laplace Equation on Polygons Setting up a Mixed Boundary Value Problem for the Laplace Equation on a Polygon A Finite Covering of a Polygon by Blocks of Three Types Representation of the Solution of a Boundary Value Problem on Blocks An Algebraic Problem The Main Result - Theorem on the Convergence of the Block Method Proofs of Theorem and Lemmas The Stability and the Labor Content of Computations Required by the Block Method Approximation of a Conjugate Harmonic Function on Blocks Neumann's Problem The Case of Arbitrary Analytic Mixed Boundary Conditions Approximate Block Method of Conformal Mapping of Polygons onto Canonical Domains Approximate Conformal Mapping of a Simply-Connected Polygon onto a Disk Basic Harmonic Functions Approximate Conformal Mapping of a Multiply-Connected Polygon onto a Plane with Cuts along Parallel Line Segments Approximate Conformal Mapping of a Multiply-Connected Polygon onto a Ring with Cuts along the Arcs of Concentric Circles Development and Application of the Approximate Block Method for Conformal Mapping of Simply-Connected and Doubly-Connected Domains Approximate Conformal Mapping of Some Polygons onto a Strip Scheme of Constructing a Conformal Mapping of a Doubly-connected Domain onto a Ring Mapping a Square Frame onto a Ring Mapping a Square with a Circular Hole Using Circular Lune Block Representation of a Harmonic Function on a Ring Using a Block-Ring for Mapping Domain (18.1) onto a Ring A Block-Bridge Limit Cases Mapping a Disk with an Elliptic Hole or with a Retro-Section onto a Ring Mapping a Disk with a Regular Polygonal Hole Mapping the Exterior of a Parabola with a Hole onto a Ring Approximate Conformal Mapping of Domains with a Periodic Structure by the Block Method Mapping a Domain of the Type of Half-Plane with a Periodic Structure onto a Half-plane Mapping a Domain of the Type of Strip with a Periodic Structure onto a Strip Mapping the Exterior of a Lattice of Ellipses onto the Exterior of a Lattice of Plates References Index.