What supplications are recited before the Adhan and before the Iqamah, and after the Adhan and after the Iqamah?

Supplicating before the Adhan or Iqamah is not legislated, and if it is specified with a particular saying or action, it is considered an innovation (bid'ah).

Supplicating between the Adhan and the Iqamah is desirable and encouraged, due to the Prophet's (peace be upon him) saying: "Indeed, supplication is not rejected between the Adhan and the Iqamah, so supplicate." Moreover, supplication immediately after the Adhan has specific formulations, among them the supplication: "O Allah, Lord of this perfect call..."

There is no evidence for supplication after the Iqamah, and specifying a supplication at this time is an innovation.

It is sunnah, upon hearing the Adhan, for the listener to repeat what the Muezzin says, except when he says "Hayya 'ala as-Salah" (Hasten to the prayer) and "Hayya 'ala al-Falah" (Hasten to success), in which case one says "La hawla wa la quwwata illa billah" (There is no might or power except with Allah).

As for supplication during the Iqamah, some scholars have held the view that it is desirable to repeat after the Muezzin by analogy with the Adhan, while others have not deemed it desirable due to the weakness of the hadith reported concerning repeating during the Iqamah. Also, saying "Aqamaha Allahu wa adamaha" (May Allah establish it and perpetuate it) when the Muezzin says "Qad qamati as-Salah" (The prayer has been established) is incorrect due to the weakness of the hadith reported in this regard.