Exim is an open-source Mail Transfer Agent (MTA): the software that routes and delivers email on Unix-like systems connected to the internet. Exim offers flexible routing and extensive checks on incoming mail, and it can replace Sendmail, although its configuration differs. It is freely available under the GNU General Public Licence and widely used by internet service providers and universities. Exim is not an end-user product with webmail or calendar, but a building block for the mail flow that you install and configure yourself.
Exim was originally developed by Philip Hazel at the University of Cambridge in the United Kingdom. The project is continued by a team calling itself The Exim Maintainers, and there is no controlling company. The United Kingdom is outside the EU, but the software runs on your own servers and processes data wherever you configure it, for example in the EU. For European organisations Exim is therefore a self-managed MTA with no licence fees or dependence on a cloud provider.