These distros listed here include only 100% free/libre software, and those that can be used with only free/libre software. They are listed in alphabetical order.
The Debian Project is an association of individuals who have made common cause to create a free operating system. This operating system that we have created is called Debian.
Debian is fully free software out of the box, however they maintain a repository of proprietary software - you can always choose not to use those.
Dragora GNU/Linux is a distribution created from scratch with the intention of providing a stable, multi-platform and multi-purpose operating system. It is built upon 100% free software. It has a very simple packaging system that allows installing, removing, upgrading and...
An independent GNU/Linux distribution based on concepts of simplicity.
Fedora creates an innovative, free, and open source platform for hardware, clouds, and containers that enables software developers and community members to build tailored solutions for their users.
Fedora is also fully free software out of the box, however there are still proprietary blobs in their kernel. It's possible to switch it out with the Linux-libre kernel.
Gentoo Linux is a versatile, fast, highly configurable and completely free Linux and FreeBSD distribution geared towards developers and network professionals.
You can always choose to build Gentoo with only fully free software included and with the Linux-libre kernel.
A purely functional package manager and an advanced distribution of the GNU operating system developed by the GNU Project—which respects the freedom of computer users.
An advanced GNU/Linux distro built on top of GNU Guix (pronounced “geeks”), a purely functional package manager for the GNU system.
The Hyperbola Project is a community driven effort to provide a fully free (as in freedom) operating system that is stable, secure, simple, lightweight that tries to Keep It Simple Stupid (KISS) with Long Term Support (LTS).
A long-term support simplicity-focused distribution based on Arch GNU/Linux.
Linux From Scratch (LFS) is a project that provides you with the steps necessary to build your own custom Linux system. There are a lot of reasons why somebody would want to install an LFS system. The question most people raise is "why go through all the hassle of manually...
Like Gentoo, you can always choose to build LFS with only fully free software included and with the Linux-libre kernel.
A project providing a fully free (as in freedom) derivative of 
Arch Linux. Inheriting Arch's lightweight and flexibility, Parabola offers software freedom plus all power to the users.
A distribution based on Arch that prioritizes simple package and system management.
A GNU distribution based on Debian with a focus on privacy, security, and convenience.
Trisquel is a computer operating system, a GNU + Linux distribution, derived from another distribution, Ubuntu, which is derived from Debian.
A GNU/Linux distribution based on Ubuntu that's oriented toward small enterprises, domestic users and educational centers.
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