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I am undergraduate student having basic knowledge of Physics. I'm looking for resources (books, video lectures, research papers, etc) to study Gravitational Waves from scratch, I think initially I should practice mathematical physics up to some extent and then proceed for GW.

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  • $\begingroup$ Because standard quantum mechanics, does not include gravity as particle with any state like a wave, everything there is more theoretical or measured indirectly, but not checked as "gravition", most measurements are a consequence of relativity $\endgroup$ – Adrian R Feb 19 '20 at 21:55
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    $\begingroup$ You have found this site, why not click the gravitational-waves tag that you've added to your question above and have a look at other questions and answers here, then go to Physics SE and click their gravitational-waves tag and read there as well. You may find that Stack Exchange itself is a helpful resource when studying from scratch (I certainly have) and you may come across something specific you'd like to ask a question about. $\endgroup$ – uhoh Feb 21 '20 at 3:21
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Gravitational waves are a prediction of Einstein's general theory of relativity, so one should be well acquainted with special relativity first, and then become familiar with basics of general relativity, and then one will be well equipped to study gravitational waves. Luckily, this should not take a long time, since there are so many great resources for relativity theory these days.

I highly recommend Ray D'Inverno's textbook on introducing Einstein's theories of relativity (special relativity is motion in the absence of gravity, general relativity is with gravity). It has introduction to the math, for example the k-Calculus that makes special relativity simpler, and for example tensor calculus in general relativity. Other approaches, like variational principle, are touched on. This is a great book meant for undergraduates. I'm not sure if you can find a free copy, you can probably find one at your library to check out, but this textbook is definitely worth the price. The chapter on gravitational waves is not only appropriate for beginners, but it also goes into depth about the basic calculations for deriving, for example, the strain of a plane gravitational-wave in a flat background spacetime (Minkowski), showing how the two polarization states of the strain and the wave equation literally fall out of the Einstein equations. This illustrates that gravitational radiation is, in principle, a metric perturbation of spacetime. This textbook is also a great intro into the mathematics of general relativity, in general, for an undergrad.

For an in-depth view of special relativity (with a chapter on curved spacetimes), see Taylor and Wheeler's classic textbook Spacetime Physics, which reads more like a comic book, honestly :). The chapters are online for free (bless Taylor and Wheeler!). I personally found this book to be very approachable and incredibly comprehensive, with lots of examples.

For technical introductions into gravitational waves and gravitational wave research, I recommend this and this (the former being more technically comprehensive but also challenging).

For nice reviews of the history of gravitational wave science, see here and here.

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My first approach would be to visit my local university library, ask for the physics section and look which books are available, e.g. with the title gravitational waves in the physics or science department. No need to read them completely, the first introductory sections are usually a good start.

If you are not feeling like going to library, why not checking the educational resources of the three big facilities which are studying gravitational waves?

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