The main research area of my PhD Thesis is History and Epistemology of Science (Physics, Mathematics, CNU 72). The combined–subjects are the History of Gravitational Waves (HGW) & the Nature of Science (NoS, CNU 70). Gravitational Waves (GW) are invisible undulations in space: any mass moves, then GW are generated through space–time radiating crossways a lake's surface. It is the main key to finally complete the Einstein's General Relativity. This thesis consists in four Parts across nine Chapters, including a large Introduction and detailed Conclusion. Including References, Appendix and Indices (Names, Subjects, Images) it totals over 700 pp. in length in an unique Vol. I examined GW through theoretical–and–experimental studies (texts analyses) into history dating as far back as the Renaissance, through to the middle of the past century, up to recent discoveries at Labs. (2015, Italy–USA, LIGO–VIRGO). The job was done in three doctoral years, including visits at the American Institute of Physics (APS, USA) and the European Gravitational Observatory (VIRGO, Italy). The main historical results of my PhD research are: 1) concept of GW which date back to Sir Clifford (1870) who conceived the geometry of space as being non–Euclidean: “[...] this property of [space] being curved or distorted is continually being passed on from one portion of space to another after the manner of a wave”, 2) first mention and related development of GW as “onde gravifique” which term was coined by Poincaré in his Sur la dynamique de l’électron (1905), 3) detailed historical comparative analysis of Clifford and Poincaré's works 4) impact of the 1957 Chapel Hill Conference on GR research, 5) development of GW detectors through the pioneering works of Weber, 6) later methods using Michelson laser interferometers that lead to building of LIGO–VIRGO, 7) the impact on Cosmology and future GW research. Other correlated results are systematically detailed in the end both of each Chapter (Final Remarks) and Parts (Epilogues). On the HGW & NoS, I examined the historical foundations of GW in order to check both specific teaching–learning difficulties & misunderstandings in modern physics and to shape curricula ad hoc at Lyceum and University. The 19th-21st century historical period is very well documented allowing me to focus on the different scientific changes that occurred at that time in an interdisciplinary way. The historical–educational goal aims to apply the framework of the Nature of Science in order to analyse & understand how the foundations of science can be used for teaching & pedagogical purposes. Relying on an appropriate series of steps to understand the evolution of science and paradigm shifts in respect to both the development of science throughout its history and the pedagogical filter of teaching–learning sciences (physics–mathematical modelling), I showed how Special/General Relativity linked to HGW may be made accessible to students. I also worked on the role played by Neurosciences/Cognitive in order to show how, by means of analogies and ad absurdum proofs within scientific teaching–learning, some notable epistemological breaks and obstacles can be overcome. I methodically collected data from my teaching at distance courses whose purpose was to introduce the main concepts of GW within the HGW framework to the students. Consequently, I analysed the data (research applied to teaching) which indicated that my experimental HGW distance course was educationally beneficial to the learners. HGW is a very new topic. It is one of the most broad and challenging subjects in the History of Science (HS & NoS): Nowadays, HGW source books lack of critical analyses in the field. The impact of my PhD Thesis in 2020 and successive related works of mine aim to assume this early research––and––pedagogical role. This thesis appeals to historians, scientists (physicists, mathematicians, applied sciences & technology), teaching experts and epistemologists.