Hello, how to update Mozila on Debian Linux? Please help me . I have 52.4 version.

It sounds like you're using Debian Stable, so you have the latest version available via the Debian repos. If you want something more current and don't mind possibly compromising the stability/security of your system, then download the latest version from Mozilla. It will be a bzipped tarball file. Decompress the file which should result in a folder; I believe the folder is named firefox. Place the folder under /home/<user>/bin. I don't know what to tell you to then get Firefox to run from your desktop as I don't know what you are using. You can probably get Firefox to run from a terminal, but I'm not sure how to do that (maybe /home/<user>/bin/firefox/firefox &) and it's probably unnecessary.

https://www.mozilla.org

Edit: If you opt to use the latest Firefox, make sure you remove the existing version from your system...

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You don't need to purge the existing firefox. The new firefox will use all the settings from the old one, but anything new in the new one will be used. I don't recommend upgrading outside the Debian repos.

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Thanks for your suggestions friends. I decided do not upgrading outside the Debian repos. thanks

Just read the following article yesterday. And no, you will not be downloading a gzipped tarball from Firefox. You'll be using the Debian Unstable repo to do this.

How to Install Firefox Quantum on Debian Stretch Linux

Edit and Caveat: It is not recommended to mix packages from Testing/Unstable in a Stable environment. Doing so can break your system. Use the above tip at your own risk.

THE PHANTOM, please be aware that debian uses the firefox ESR versions.
from a security & stability point of view, those are actually better than the newest upstream release.
and if there's a problem, they get updated pretty fast!
there's no harm in using firefox ESR on debian!

that said, if you really feel you need version 57, there are ways, however i do not recommend this:
watchingu, i liked your previous reply (post #2) better.
let me explain:
the article is well explained, and i suppose they did it "properly" (apt pinning etc.), but nevertheless it is playing with sources, mixing stable and unstable, and never actually mentions the extreme dangers that holds.

so, unless op knows what they're doing 111%, i'd rather recommend the approach of downloading, unzipping, running the executable as shown in post #2.

But we want the shiny new toys!

I agree. I've been planning to come back and edit my last post. It is not recommended to mix packages from Testing/Unstable in a Stable environment. Doing so can break your system. The correct method would be to backport the lastest Firefox, if possible.