Books must be chosen carefully.

Literal

Books [topic-は], carefully choose-must.

注意深く is the adverbial form of the い-adjective 注意深い ('careful, attentive,' literally 'attention-deep'). ~なければなりません is the polite form of ~なければならない, the most formal of the several Japanese 'must' expressions. The topic-comment construction with は + comma gives the sentence a measured, essay-like tone.