May and would in such expressions were originally subjunctives; would stands for I would, that is, I should wish. Want in the first example is an infinitive without to ([§ 311]). For wishes expressed by the infinitive, see [§ 320].

278. Exhortations in the first person plural sometimes take the subjunctive in elevated or poetical style.

Exhortation is ordinarily expressed by let us followed by the infinitive without to.

Let is a verb in the imperative mood, us is its object, and the infinitive (join, have, camp) depends on let.

Subjunctives in Concessions, Conditions, etc.

279. The subjunctive is used after though, although, to express an admission or concession not as a fact but as a supposition.