This monograph systematically treats a theory of elliptic boudary value problems in domains without singularities and in domains with conical or cuspidal points. This exposition is self-contained and a priori requires only basic knowledge of functional analysis. Restricting to boudary value problems formed by differential operators and avoiding the use of pseudo-differential operators makes the book accessible for a wider readership. The authors concentrate on fundamental resultsof the theory: estimates for solution in different function spaces, the Fredholm property of the operator of the boundary value problem, regularity assertions and asymptotic formulas for the solutions near singular points. A special feature of the book is that the solutions of the boundary valueproblems are considered in Sobolev spaces of both positive and negative orders. Results of the general theory are illusrtrated by concrete examples. The book may be used for courses in partial differential equations