Gravitational waves were predicted by Albert Einstein in his most famous theory, the general theory of relativity, but it took almost a century for these waves to be detected and their existence proven. This book introduces gravitational waves and discusses some of their applications in five dimensions, this is all done in classical gravity. It also explains gravitational waves in quantum gravity (in which the universe is considered to be not continuous) and implications for trying to understand and explore dark energy and an expanding accelerated universe.