The Erasmus Mundus program is a European Union initiative aimed at strengthening higher education and building stronger bonds between Europe and the rest of the world.
Most importantly, there are a number of scholarships available through Erasmus Mundus for Europeans as well as citizens of other countries. These are at the master's level (i.e. for students who have already completed or are about to complete their bachelor's degree).
Tuition, travel, and living expenses are all covered. Students will typically even be provided with an E.U. work visa on graduation in case they want to gain practical experience in their new field instead of returning home immediately.