Question: What is the best textbook (or book) for studying Etale cohomology?

Answer: 
I'll complement the list of well known books on the subject by some freely available documents, which I find user-friendly. 

[Here](http://stacks.math.columbia.edu/download/etale-cohomology.pdf) are great lecture notes , from a course that de Jong (of Stacks Project fame) gave in 2009. 

Edgar José Martins Dias Costa's [short dissertation](https://dspace.ist.utl.pt/bitstream/2295/686086/1/tese.pdf)  on the subject . 

Evan Jenkins's [notes](http://www.math.uchicago.edu/~ejenkins/etale.html) of a seminar on étale cohomology (click on the pdf icons).

The [arXiv notes](http://arxiv.org/PS_cache/arxiv/pdf/1101/1101.0683v1.pdf)  of a mini-course given by a fine expositor, Antoine Ducros, which also cover analytical aspects of étale cohomology (used for Berkovich spaces). 

And finally a [historic survey](http://www.math.u-psud.fr/~illusie/Grothendieck_etale.pdf) (in French unfortunately) on the genesis and successes of étale cohomology.  

 It was written by Illusie, one of Grothendieck's most brilliant students, who acknowledges the help he received in his reminiscences from luminaries such as Serre and Deligne.
Here are some extra references:

* [Amazeen, Étale and Pro-Étale Fundamental Groups](http://page.mi.fu-berlin.de/lei/finalversion%20(1).pdf);
* [Belmans, Grothendieck Topologies and Étale Cohomology](https://pbelmans.ncag.info/notes/etale-cohomology.pdf);
* [Bergström--Rydh, Étale Cohomology Spring 2016](https://people.kth.se/~dary/etale-cohomology/);
* [Conrad (?), Étale Cohomology](https://www.math.ru.nl/~bmoonen/Seminars/EtCohConrad.pdf);
* [Hajj Chehade, Sheaf Cohomology on Sites and the Leray Spectral Sequence, Chapter
3](http://www.math.leidenuniv.nl/scripties/hajj.pdf);
* [Klingler, Étale Cohomology and the Weil Conjectures](https://webusers.imj-prg.fr/~bruno.klingler/cours/Weil.pdf);
* [Kunkel, Étale Fundamental Group: An Exposition](http://www.math.harvard.edu/theses/senior/kunkel/kunkel.pdf);
* [Laskar, Étale Cohomology](http://algant.eu/documents/theses/laskar.pdf);
* [Puttick, Galois Groups and the Étale Fundamental Group](https://webusers.imj-prg.fr/~jean-francois.dat/enseignement/memoires/M1AlexPuttick.pdf);
* [Robinson, Étale Cohomology](https://www.the-paper-trail.org/wp-content/uploads/2014/03/EC-Essay-1.pdf);
* [Sarlin, The Étale Fundamental Group, Étale Homotopy and Anabelian
Geometry](http://kth.diva-portal.org/smash/get/diva2:1165816/FULLTEXT01.pdf);
* [Szamuely, Galois Groups and Fundamental Groups, Chapter 5](https://www.cambridge.org/br/academic/subjects/mathematics/algebra/galois-groups-and-fundamental-groups-1);
* [The Stacks Project Authors, Étale Cohomology](https://stacks.math.columbia.edu/download/etale-cohomology.pdf);
* [Yang, Fundamental Groups of Schemes](https://www.math.u-bordeaux.fr/ALGANT/documents/theses/yang.pdf);
* [Zarabara, Étale Cohomology over $\mathrm{Spec}(k)$](http://algant.eu/documents/theses/zarabara.pdf).