The Erasmus programme encourages students to move out to other countries’ universities and follow a programme of higher education. The exchange of students is understood to strengthen European co-operation and intercultural understanding.
See here how the European Commission describes the programme (link):
The Erasmus Mundus programme is a co-operation and mobility programme in the field of higher education. It aims to enhance quality in European higher education and to promote intercultural understanding through co-operation with third countries.
Erasmus Mundus was first introduced in July 2001, when the European Parliament and Council received a Communication by the European Commission on strengthening EU-third country co-operation in higher education. Following the positive reception of the Communication, the Commission adopted a programme proposal, Erasmus World in July 2002. The programme was then renamed Erasmus Mundus. “Mundus” is the Latin word for “world”.
On 5 December 2003, the Erasmus Mundus programme Decision was adopted and published in the European Union’s Official Journal on 31 December 2003 and entered into force on 20 January 2004.
