  In this manuscript we review the theoretical foundations of gravitational
waves in the framework of Albert Einstein's theory of general relativity.
Following Einstein's early efforts we first derive the linearised Einstein
field equations and work out the corresponding gravitational wave equation.
Moreover we present the gravitational potentials in the far away wave zone
field point approximation obtained from the relaxed Einstein field equations.
We close this review by taking a closer look on the radiative losses of
gravitating $n$-body systems and present some aspects of the current
interferometric gravitational waves detectors. Each section posses a separate
appendix-contribution where further computational details are displayed. To
conclude we summarize the main results and present a brief outlook in terms of
current ongoing efforts to build a spaced based gravitational wave observatory.
