Verb "pouvoir": a semi-auxiliary
In French, avoir and être are the main auxiliaries but there are also semi-auxiliaries, capable of significantly changing the meaning of a verb. Thus, when it is followed by an infinitive, pouvoir expresses a nuance of possibility.
Two forms at present
It should also be noted that the verb "pouvoir" has two forms in the indicative present: Je peux and je puis.
The last one is much more formal and is hardly used in everyday conversation except when a question is asked where it says : est-ce que je peux or puis-je ? In the same way, the last form is much more polished.
It should also be noted that "pouvoir" endings at indicative present are irregular: je peux, tu peux, il peut. LThe particularity is to take an x instead of an s or an e like most other verbs. Other such verbs are "faillir" (to fail), "vouloir" (to want) and "valoir" (to be worth).
Imperative
The verb pouvoir does not exist in the imperative. To replace it, we use the subjunctive: Puisses-tu trouver la solution, puissions-nous, puissiez-vous.