Theory of a Higher Order Sturm Liouville Equation This book develops a detailed theory of a generalized Sturm Liouville Equation which includes conditions of solvability classes of uniqueness positivity properties of solutions and Greens functions asymptotic properties of solutions at infinity. Of independent interest the higher order Sturm Liouville equation also proved to have important applications to differential equations with operator coefficients and elliptic boundary value problems for domains with non smooth boundaries. The book addresses graduate students and researchers in ordinary and partial differential equations and is accessible with a standard undergraduate course in real analysis