ymarks browser extension:

Support for your browser is under way. :-)

Please note that these downloads are alpha-quality as it stands. Do not use them in production just yet.

ymarks is a free and open source add-on for several modern web browsers, licensed under the terms of the WTFPL, with a server component written in C that allows you to synchronize your browser's bookmarks with an SQLite3 database that can be hosted either on your local machine or somewhere in your intranet (or even the internet). It is supposed to be a single-user system in order to reduce complexity and increase privacy, but you can (technically) run as many parallel instances of ymarks as you like.

Alternatives: had an article about potential alternatives if you can't stand ymarks.
A NANY 2018 project.