Matrix.org’s reference server – Synapse: https://github.com/matrix-org/synapse
To install, first take a look at Installing Synapse
You can use the matrix-docker-ansible-deploy to easily install Synapse and related dependencies using pre-build Ansible playbooks and docker images.
Apt repo: https://packages.matrix.org/debian/
ArchLinux package from Ivan Shapovalov: https://www.archlinux.org/packages/community/any/matrix-synapse/
There is a FreeBSD package port available as net-im/py-matrix-synapse/.
Synapse is also on the Open Build Service.
Synapse is available for the Nix package manager.
You can get Synapse on Yunohost
Synapse is available in the FreedomBox distribution (version 0.14.0 or later).
There is also a handy spreadsheet to calculate HDD space for your Synapse instance.