The numerous publications on spline theory during recent decades show the importance of its development on modern applied mathematics. The purpose of this text is to give an approach to the theory of spline functions, from the introduction of the phrase spline by I.J. Schoenbergin 1946 to the newest theories of spline-wavelets or spline-fractals, emphasizing the significance of the relationship between the general theory and its applications. In addition, this volume provides material on spline function theory, as well as an examination of basic methods in spline functions. The authors have complemented the work with a reference section to stimulate further study.