In this thesis two-point Sturm-Liouville boundary value problems are considered. They occur frequently in mathematical physics, e.g. when solving a heat conduction problem in a solid bar by the method of separation of variables. These problems consist of a differential equation [p(x)y´]´−q(x)y+λr(x)y = 0, 0 < x < 1, together with the separated boundary conditions \(α_{1}y(0)+α_{2}y´(0) = 0\), \(β_{1}y(1) + β_{2}y´(1) = 0\). If the functions p, p´, q, and r are continuous on the interval 0 ≤ x ≤ 1, and p(x) > 0 and r(x) > 0 holds at all points in 0 ≤ x ≤ 1, then these problems are called regular. Major properties of such problems and their solutions are discussed in Chapter 4. In the following chapters we are interested in extending and generalizing the problems considered. In Chapter 5 we indicated how to deal with nonhomogeneous equations and more general boundary conditions. Chapter 6 is devoted to singular Sturm-Liouville problems where the coefficients p, q, and r in equation do not quite satisfy the rather strict continuity and positivity requirements. In the last chapter we examine posing the problems, solved by the method of separation of variables, in various geometrical regions. The emphasis is on those leading to singular Sturm-Liouville problems when the variables are separated.