Effective field theories of post-Newtonian gravity: a comprehensive review

This review article presents the progress made over the last decade, since the introduction of effective field theories (EFTs) into post-Newtonian (PN) gravity. These have been put forward in the context of gravitational waves (GWs) from the compact binary inspiral. The mature development of this interdisciplinary field has resulted in significant advances of wide interest to physics at several levels serving various purposes. The field has firmly demonstrated, that seemingly disparate physical domains, such as quantum field theory and classical gravity, are related, and that the EFT framework is a universal one, where it has been proven to supply a robust methodology to boost progress in the development of PN theory. In this review emphasis was put on an accessible pedagogic presentation of the field theoretic aspects of the subject, with the view, that these are in fact common across the whole of theoretical physics, rather than in their original narrow quantum context. The review is aimed at a broad audience, from general readers new to the field, to specialists and experts in related subjects. *To my loving father, sister, and old friend, who is a brother to me.