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The purpose of this thesis is to calculate the relativistic correction to thegravitational waves produced by compact binaries in the inspiral phase. Thecorrection is up to the next to leading order, the so-called firstpost-Newtonian order (1PN), which are correctional terms proportional to$(v/c)^2$ compared to leading order, Newtonian, terms. These corrections arewell known in the literature, even going beyond the first order corrections, sowhy is it computed again here? In later years, an alternative approach forcomputing these terms using effective field theory has emerged. This thesisinvestigates this approach by replicating it, and attempts to make thisapproach more accessible to those not familiar with effective field theories.It has been claimed that this approach greatly simplifies the complicatedcalculations of gravitational waveforms, and even provides the requiredintuition for 'physical understanding'. By this master student that was foundnot to be entirely correct. The calculations were made easier for those with arich background in quantum field theory, but for those who are not wellacquainted with quantum field theory this was not the case. It was, however,found to be a worthwhile method as a means for deepening one's understanding ofgravity, and might provide a shorter route for some alternative theories ofgravity to testable predictions.

First post-Newtonian correction to gravitational waves produced by  compact binaries: How to compute relativistic corrections to gravitational  waves using Feynman diagrams