What are the obligatory remembrances (adhkar) reported from the Messenger of Allah, peace and blessings be upon him, that a Muslim should adhere to?

Allah has encouraged abundant remembrance (dhikr) and made success (falah) contingent upon it. This is emphasized in the restricted (muqayyad) forms of dhikr. There are also obligatory forms of dhikr, such as uttering the two Shahadas, the opening takbir (takbirat al-ihram), and the salutation (taslim) in prayer, returning the salutation, and the tashahhud according to some scholars. Also, sending blessings upon the Prophet (peace be upon him) when he is mentioned or his name is heard, or in the tashahhud, or in gatherings, according to some scholars. And the talbiyah in Hajj and Umrah, the tasmiyah (uttering 'Bismillah') when slaughtering an animal, and the adhan and iqamah according to some.