〜べきだ／べきではない
Should, ought to (duty); べきではない: should notmachine translation
FormationVerb dictionary form + べきだ (する → するべき／すべき)
〜べきだ expresses what the speaker believes is the RIGHT THING TO DO in terms of morality, duty, or principle: 約束は守るべきです (a promise should be kept). The negative form 〜べきではない means "one shouldn't — morally, it's not acceptable": 人の手紙を勝手に読むべきではない.
Connection: verb dictionary form + べきだ; する alone has two equally correct forms: するべき or すべき. Because べきだ is a rather forceful judgment, avoid using it directly with superiors — it sounds like you're lecturing them.
Distinguishing within the N3 advice group: ことだ is advice for one person in a specific situation, ものだ・ものではない invokes society's common sense, while べきだ is the speaker's own conviction about right and wrong. Compared with 〜なければならない, which you've already learned — an objective obligation imposed by rules or circumstances — べきだ is subjective: violating べきだ makes you morally blameworthy, but not necessarily a lawbreaker.
Examples
学生はもっと本を読むべきだ。
Students should read more books.
約束は守るべきです。
A promise should be kept.
人の手紙を勝手に読むべきではない。
You shouldn't read other people's letters without permission.