Matrix.org’s reference server – Synapse: https://github.com/matrix-org/synapse
Apt repo: https://matrix.org/packages/debian/
Dockerfile from Silvio Fricke: https://registry.hub.docker.com/u/silviof/docker-matrix/ – also hosted on https://github.com/matrix-org/docker-matrix
ArchLinux package from Ivan Shapovalov: https://aur.archlinux.org/packages/matrix-synapse
There is a FreeBSD package on freshports.org.
Martin Giess has created an auto-deployment process with vagrant/ansible, tested with VirtualBox/AWS/DigitalOcean – see https://github.com/EMnify/matrix-synapse-auto-deploy for details.
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.