。
I have to register for my courses by tomorrow.
Literal
Tomorrow [by-までに] take [to-する] courses [possessive-の] registration [object-を] must.
履修する科目の登録 is a dense noun phrase: 'registration of courses to be taken.' までに marks the deadline — 'by tomorrow.' ~なければなりません is the polite obligation form. Note the sentence as written contains a typo — なりまれん should be なりません.