In 1905 Albert Einstein presented his Theory of Special Relativity with two postulates that led to a new realm of reasoning and observing the universe. Eleven years later Einstein extended these postulates to form the General Theory of Relativity. This theory predicts the existence of gravitational waves and describes properties these waves must have. If such gravitational waves could be detected, they could reveal much about the physics and history of the universe. In the years since their prediction, many attempts have been made to detect these elusive waves. As of yet we have failed to do so in any reproducible manner. In recent years renewed effort and the aid of technological advances have rekindled excitement to detect Einstein's gravitational waves. Gravitational waves are disturbances in the curvature of spacetime caused by accelerating matter. The wave is an oscillation or ripple traveling at, or near, the speed of light through the fabric of spacetime. This propagation can be compared to the ripples on the surface of a pond caused by dropping a stone. Gravitational waves also ripple away from their source. As the gravitational waves travel through intervening matter in space, they lose strength proportional to the square of the distance from their source. 1 Gravitational waves are produced by large-scale and non-spherical vibrations of spacetime caused by accelerating matter. 2 Sources of gravitational waves can be found in various forms throughout the universe. We will describe five such sources of gravitational waves. The first source we discuss is that of orbiting masses. One such source is a binary star system. General relativity predicts that some of the star's orbital energy dissipates as gravitational radiation. 3 As the binary system emits gravitational waves its orbital period decreases. For example, Hulse and Taylor observed the decelerating orbital motions of the neutron binary star system, PSR 1913+16. They showed that this predicted loss...