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://matrix.org/packages/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
There is also a handy spreadsheet to calculate HDD space for your Synapse instance.