The documentation required for studying in Denmark depends on your country of origin and the duration of your stay. Nordic citizens do not need a passport to enter Denmark while EU/EEA citizens do not require anything more than a valid passport to enter Denmark (although some action may need to be taken on arrival). Meanwhile, non-EU/EEA students will need a visa/residence permit.
EU/EEA and Swiss nationals
Students from the EU/EEA and Switzerland may reside in Denmark for up to three months without any further documentation than a valid passport. Those planning on staying longer than three months will need a Danish registration certificate. A registration certificate can be obtained from the Regional State Administration and you will need to apply for it within three months of your arrival.A registration certificate makes it possible to get a personal identification number and a health insurance card.
If you are from outside the EU/EEA, then the kind of permit you need to study in Denmark will depend on the duration of your stay. For a short stay of less than three months, students will require a visa, and for a long stay of more than three months a residence permit is required.