Formal, literary prohibition used at the end of a sentence. Equivalent to ～してはいけない in modern Japanese.
ここに立ち入るべからず。
You must not enter here.
この書類を外部に持ち出すべからず。
These documents must not be taken outside.
Rare, formal or literary expression of impossibility. In modern Japanese, ～できない is far more common.
この問題は解くべからず。
This problem cannot be solved.
べからず is the negative classical form meaning 'must not / shall not', the direct opposite of the obligation sense of べし.
Derived from the classical auxiliary verb べし (beshi) in its negative form べからず (bekarazu), meaning 'must not' or 'cannot'. The form is now largely restricted to formal written language.