In Germany, a prerequisite (and also the traditional route) to enrollment into a tertiary level education institution (university, university of applied sciences a.k.a. ‘Fachhoschule,’ college of art and music, etc) is a passing score on the final examination whereby a certificate called the ‘Abitur’ (or Fachabitur) is obtained. As a general rule, Abitur – formally enabling students to attend a university – is necessary for enrollment into most universities, but exceptions to this rule are not infrequent (one of the alternative routes is a passing score on the ‘Begabtenprüfung’ a.k.a. ‘the aptitude test’).
As an international student, however, you need to apply well in advance in order for the International Students Office (Akademisches Auslandsamt) to consider your application – including previous academic record – and determine whether it meets all admission requirements; for this purpose you will need to produce proof of completion of secondary education (e.g. high school diploma, ‘Matura,’ ‘A-Levels,’ or if required in your country, proof of having passed a university entrance examination) that is an equivalent of Abitur.
As to whether your high school diploma gets accepted for purposes of studying in Germany, depends on what country it was issued in; if your high school diploma was issued in a EU or EEA member country, then it is accepted for direct application at a university, otherwise you may have to undergo (again depending on the country of issuance of your high school diploma) a ‘Feststellungsprüfung’ assessment examination, after having attended a Studienkolleg (preparatory course).
For further details go to https://www.daad.de/deutschland/nach-deutschland/voraussetzungen/en/6017- university-admission-and-requirements/?id=1&ebene=1
Certain universities of applied sciences a.k.a. ‘Fachhoschulen,’ may require that you complete a working internship prior to enrolling.
In order to be admitted to a post-graduate (Master’s or Ph.D.) program, a formal recognition of your university degree is required, from your home country or another country.