〜ましょう

〜ましょう is the polite-register volitional / suggestive — "let's do X" when offered as an invitation, or "shall I / shall we do X" when offered as a tentative proposal. 行きましょう = "Let's go" or "Shall we go?" depending on intonation.

The plain-form counterpart is 〜よう / 〜おう (行こう, 食べよう). The polite form is used in mixed-status group situations, formal contexts, and with strangers. In casual speech among peers, plain volitional is the default.

Attached to a question particle か, 〜ましょうか becomes a soft offer: 手伝いましょうか — "Shall I help?" This is one of the most polite ways to volunteer assistance in Japanese — the か removes the assumption that the offer will be accepted, leaving the listener room to decline gracefully.

The form attaches to the same i-form base as ます: 食べ + ましょう, 行き + ましょう, 来 + ましょう, し + ましょう.