What should be in a motivation letter? What are the goals?

I would like to go an Erasmus exchange to ETH Zurich next year (CS Artificial intelligence) but there is only one spot and more than one person that wants to go.

I have read motivation letters of others, even specific for an erasmus exchange, but some things are still quite vague. The letter is sent to the faculty at my university, this is not yet an application at ETH itself. This is for the selection procedure for an Erasmus exchange.

• What information should the letter contain?


• What should the letter convince the faculty of?


• What experiences should I mention? (see below)


• How do I convice the faculty to pick me?


• Should I include recommendation letters? From whom?

Any other tips for an motivation letter are welcomed too, of course.

Background information: Me

For my age (20), I have a relatively (to the students in my year) substantial experience. (Of course these experiences are only the provable ones.)

• Top 5% of my year.


• Internship at the university (robotics though, not AI)


• Was a board member at a non-profit (responsible for the IT side of the company).


• Studied abstract maths alongside the regular curriculum, specifically to have a better background for CS.