A theory of generalized Cauchy-Riemann systems with polar singularities of order not less than one is presented and its application to study of infinitesimal bending of surfaces having positive curvature and an isolated flat point is given. The book contains results of investigations obtained by the author and his collaborators.

Introduction
Interrelation Between Sets of General and Model Equation Solutions.
The Model Equation
The General Equation
Modified Generalized Cauchy-Riemann Systems with a Singular Point
Generalized Cauchy-Riemann System with the Order of the Singularity at a Point Strictly Greater Then 
1. Infinitesimal Bendings of Surfaces of Positive Curvature with a Flat Point.
Supplement-Generalized Cauchy-Riemann Systems with a Singular Line.

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