Why do people start repeating the Takbir at the beginning of the Adhan, and is their action correct, given that the Prophet (peace and blessings be upon him) said: "When he says: Allahu Akbar, Allahu Akbar, then say: Allahu Akbar, Allahu Akbar," which implies that the repetition should be after the muezzin finishes the Takbir?

The Sunnah for repeating the Adhan is for the listener to say exactly what the Mu'adhdhin says, except when he says: "Hayya 'ala as-Salah (Hasten to prayer)" and "Hayya 'ala al-Falah (Hasten to salvation)," at which point the listener says: "La hawla wa la quwwata illa billah (There is no might nor power except with Allah)." The proof for this is the hadith of Umar ibn al-Khattab, may Allah be pleased with him, that the Prophet, peace and blessings be upon him, said: "When the Mu'adhdhin says: 'Allahu Akbar, Allahu Akbar,' one of you should say: 'Allahu Akbar, Allahu Akbar.' Then when he says: 'Ashhadu an la ilaha illallah,' he should say: 'Ashhadu an la ilaha illallah.' Then when he says: 'Ashhadu anna Muhammadan Rasoolullah,' he should say: 'Ashhadu anna Muhammadan Rasoolullah.' Then when he says: 'Hayya 'ala as-Salah,' he should say: 'La hawla wa la quwwata illa billah.' Then when he says: 'Hayya 'ala al-Falah,' he should say: 'La hawla wa la quwwata illa billah.' Then when he says: 'Allahu Akbar, Allahu Akbar,' he should say: 'Allahu Akbar, Allahu Akbar.' Then when he says: 'La ilaha illallah,' he should say: 'La ilaha illallah' from his heart, he will enter Paradise." Narrated by Muslim.

It is recommended for the listener to say each word immediately after the Mu'adhdhin finishes it. Some scholars have permitted repeating the Adhan before the Mu'adhdhin if the person is busy or if the Mu'adhdhin is slow, although the best is to repeat after the Mu'adhdhin. Others have held the view of sufficing with repeating the Adhan up to the end of the Shahadatayn without adding for "Hayya 'ala as-Salah" and "Hayya 'ala al-Falah." Therefore, merely repeating "Allahu Akbar, Allahu Akbar" is not sufficient. As for repeating the Adhan quickly without following the Mu'adhdhin, some scholars consider it valid, though it is less preferred.