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I'm not very advanced in LaTeX. I don't know what e.g. XeLaTeX or LaTeX->dvipdfmx are. I only use ShareLaTeX and used to use Overleaf.

I need to be able to insert thumbnails in a document which when clicked would display their bigger version in a popup or something.

This gif is a perfect example of what I want to achieve.

Is it possible to achieve something like that in one of the mentioned sites? If so, how? (if there's a way to achieve it online but on a different site, I'm still interested)

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ShareLaTeX and Overleaf are just online-editors. The PDF format allows for such effects, but only few PDF viewers may be able to show the effect when reading the ready PDF document, most likely Acrobat Reader.

See e. g. https://tex.stackexchange.com/a/12293 which defines a \zoombox{...} command.

A zoomable "thumbnail" could be inserted as:

\zoombox{\includegraphics[width=1cm]{my_image_file}}

If you use an online LaTeX editor, you will have to download the final PDF and open it in Acrobat Reader.

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