There are many web browsers available for everyone’s use that are based on the open-source Mozilla Firefox browser code. For example, WaterFox, Palemoon and Comodo IceDragon are all based on the Firefox code. Ever since Mozilla decided to make some very drastic changes in the Firefox web browser through the Quantum update, these other Firefox based browsers have become a little more popular as they use an older Firefox code and allow you to use your favorite browser extensions that no longer worker in the latest version of Mozilla Firefox. I personally use Palemoon browser for some websites as it not consume excessive amount of memory on those sites.
The developers of Palemoon browser have now released another web browser called Basilisk browser. While Palemoon and Basilisk are both based on the Firefox code for version 52.9, there are many differences between the two. Basilisk uses many new components developed by Palemoon developers such as the Goanna as the web rendering and layout engine (Palemoon uses Gecko), UXP as a replacement of the older XUL platform and more.
The main aim of Basilisk browser development is to provide users an option to have modern web browser while keeping all the useful features that are no longer available in the newer versions of Mozilla Firefox browser. For example, Basilisk does not use multi-process browsing (also called Electrolysis in Firefox) and uses the old fashioned single process web browsing.
Basilisk does not requires the extensions files (XPI) to be signed so that you can use the older extensions for Firefox can be used in Basilisk without any trouble. One of my favorite extension, DownThemAll, that no longer works in the new versions of Mozilla Firefox browser, works perfectly well in Basilisk browser.
While Basilisk keeps the older features from Firefox, it does not compromise on the security front at all. It has updated the security in Basilisk and supports newer web cryptography such as TLS 1.3, HSTS etc.
You can download Basilisk from https://www.basilisk-browser.org/.