You do not need an entry visa in order to study in Germany if you are a citizen of an EU country, Iceland, Liechtenstein, Norway or Switzerland. You do not need an entry visa if you come from Australia, Andorra, Brazil, El Salvador, Honduras, Israel, Japan, Canada, Monaco, the Republic of Korea, New Zealand, San Marino, the United Kingdom of Great Britain and Northern Ireland or the United States of America either.
All other international students require a visa in order to enter Germany for the purpose of studying.
You can find out what criteria you must meet in order to be issued a visa by visiting the "Visa for studying" section.