Abstract
Continued fractions constitute a very important subject in mathematics. Their importance lies in the fact that they have very interesting and beautiful applications in many fields in pure and applied sciences. This review article will reveal some of these applications and will reflect the beauty behind their uses in calculating roots of real numbers, getting solutions of algebraic Equa tions of the second degree, and their uses in solving special ordinary differen tial Equations such as Legendre, Hermite, and Laguerre Equations; moreover and most important, their use in physics in solving Schrodinger Equation for a certain potential. A comparison will also be given between the results ob tained via continued fractions and those obtained through the use of well-known numerical methods. Advances in the subject will be discussed at the end of this review article.