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The book provides a clear understanding of the subject of approximation of eigenvalues of ordinary differential operators.This study will provide useful information which can be used to project the direction and extend the results of J. Weidmann. The study of Sturm-Liouville differential operators are found to have applications in several branches of mathematical physics and quantum mechanics. Chapter II is concerned with linear operators and Sturm-Liouville differential expression. Chapter III deals with self- adjoint extension of Sturm-Liouville differential operators.Chapter IV deals with some advanced results about the generalized strong convergence of self-adjoint operators.