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Al-Ṭayyib Abū'l-Qāṣim ibn al-Manṣūr (Arabic: الطيب أبو القاسم بن المنصور) was, according to the Mustaali sect of Isma'ilism, the twenty-first Imam and the last Caliph of the Fatimid Caliphate. Abul-Qāṣim was the son of the twentieth Fatimid Imam, al-Amir bi-Ahkami'l-Lah, who ruled Egypt from 1101-30. He was born in Cairo on Sunday, March 16, 1130 (4th Rabi' al-thani, 524 AH) and was 2 years 7 months old when his father, al-Amir, was assassinated in the night of (Thursday, October 15, 1132, 4th Dhu al-Qi'dah, 526 AH). Tayyib was reported to be about two years old at the time of al-Amir's assassination. Al-Hafiz was appointed representative Caliph on behalf of Imam Al-Tayyib. Later al-Hafiz declared himself as Imam and Caliph in 528 AH/1134 AD and Al-Tayyib was taken into hiding. 
Birth and Infancy
As per chronicle of Ibn al-Muyassar(d.677): "In Rabi al-awwal(of..524 AH)..Abul Qasim al-Tayyib was born to al-Amir;...Cairo was decorated..New suits of clothes were issued to the troops...at the 'aqiqa ceremony... in presence of al-Amir...child was brought in, and Chief Qadi Ibn al- Muyassar was given the honour of holding it...the palace was filled with fruits and other sweets..."
It is said that the guardian of Tayyib was Ibn Madyan, who have hidden him in a mosque Masjid ur-Rahmah. The infant son of al-Amir was supposed to carry in a basket of reeds by Abu Turab in which were vegetables (‘dishes of cooked leeks and onions and carrots’), and the baby wrapped in ‘swaddling clothes was on the bottom with the food above him, and he brought him to the cemetery and the wet nurse suckled him in this mosque, and he concealed the matter from al-Hafiz until the baby grew up and began to be called Kufayfa, “little basket.”’ 
According to Ṭayyibī Musta‘lid tradition, before Ṭayyib went into the Occultation, his father al-Amir had instructed Queen al-Hurrah Arwa bint Ahmad in Yemen to anoint a vicegerent after the seclusion, the Da'i al-Mutlaq, who as the Imam's vicegerent has full authority to govern the community in all matters both spiritual and temporal.
Hafizi Mustaali Ismailis continued to accept the legitimacy of the Fatimid rulers and Hafizi Ismaili Imams (see Hafizi) of Egypt between 1130-1171 and after the fall of the Fatimid caliphate instead of aṭ-Ṭayyib Abī l-Qāṣim.
Tayyibi in Yemen
There was a sijill (Royal order)(524 AH) of al-Amir to Yemen('testimony of al- Khattab available) 'announcing birth of the heir al- Tayyib in the court of al- Mallika al-Sayyida(Arwa al-Sulayhi)' by 'Egyptian envoy' Muhammad b. Haydara. On the occasion of the commemoration of the murdered Imam, the envoy said: "..appointed by his(Amir) nass...al-Imam al-Tayyib...it is in vein that mislead people think it will diminish by your(Amir) death.." Later in 526 AH, Abd al Majid in his official correspondence to Queen Arwa al-Sulayhi declared himself 'Amir al- Mumineen(leader)' in place of 'Wali-e-ahd(representative) al-Muslimeen'. According to this ueen al-Hurrah Arwa al-Sulayhi found it a betrayals as per the earlier sijill of Imam al Amir and of Abd al Majid himself declaring 'Abd al Majid a Wali of the Imam'.
As per 'Uyun al Akhbar', "She (Queen Arwa al-Sulayhi) never ceased remain faithful to al-Tayyib. In the preamble of the will, it enumerated all the Imams; the list ends with al-Tayyib. The text gives a detailed description of the Queen's jewellery brought for the inspection, all the jewellery is bequeathed, as a qurban, to the Imam al-Tayyib, Al-Ahmad..al-Sulayhi is appointed as executor; his duty is to deliver the jewels, after the Queen's death, ..at the Gate of the Friend of God(bab-ul- wali-ul-llah), ..to the person that will be appointed by the order of the Imam(Tayyib) to receive them...". She anointed Da'i al-Mutlaq / vicegerent on behalf of Imam Tayyib. The Dai al-Mutlaq would have full authority to govern the community in all matters both spiritual and temporal, and Dai Zoeb bin musa was designated first for the post with Ibrahim as his assistant who has taken over next Dai after the death of Zoeb. Hafizi followers report that the Zurayids were the subsequent head of the Hafizi party in Yemen.
The line of the Da'is continued until the 24th Dai Yusuf Najmuddin ibn Sulaiman in Yemen. On behalf of Da'i of Yemen, there were Wali ("representative" or "caretaker") of the Fatimid Dawat appointed in India. Moulai Abadullah(covered North India) and Moulai Nuruddin (covered South India) were first two to influence in India and initiate Ismaili Tayyibi Faith. Syedi Fakhruddin son of Vazir Tarmal of King Sidhraj of Gujrat(1094-1134AD) who accepted the Islamic faith was prominent, covered Rajasthan. His Mausoleum is in Galiakot and visited by all the area people irrespective of their cast.
In 1592, the Taiyabi broke into two factions in a dispute over who should become the twenty-seventh Da'i: Dawood Bin Qutubshah or Sulayman bin Hassan. The followers of the former, primarily in India, became the Dawoodi Bohra, the latter the Sulaymani of Yemen. In 1637, the Alavi Bohra split from the Dawoodi bohra community.
Due to prosecution by the local ruler in Yemen, the Dawat then shifted to India under the 25th Da'i Jalal Shamshuddin. This is continued till date (As of March 2015[update]), and at present the largest Taiyabi-descended faction is the Dawoodi Bohra Da'wa. The other factions of Sulaimani Bohra are headed by their 52nd Da'i Al-Fakhri Abdullah, and the Alavi Bohra are headed by their 45th Da'i Haatim Zakiyuddin.
Hafizi Mustā‘lī Ismāʿīlīs were those who continued to accept the legitimacy of Hafiz as Fatimid Imam of Egypt between 1130-1169 instead of Imam aṭ-Ṭayyib Abī l-Qāṣim. After the end of their rule by Saladin they are apparently extinct. But the Tayyibi follower of Imam Tayyib continued in Yemen and Indian subcontinent.
Tayyib amongst Shia Islam
Time line indicating Imam amongst other Shia Imam:
- "al-Amir was killed on Tuesday", p.198; "the ʿUyun has Tuesday the 3rd Dhu-l-qaʿda" p.195, footnote; The Succession to the Fatimid Imam al-Amir; By: S M Stern; BRILL
- "Musta'alins". ismaili.net.
- "Nizar I (487-490/1095-1097), 19th Imam". ismaili.net.; "infant son of al-Amir is named Tayyib, about two and half years old"
- The succession of the Fatimid Imam al-Amir; by: S M Stern; p.200-201, according to the Uyun al-akhbar: "Abd al-Majid, too, showed signs of apostasy (nifaq) and aspired to sovereignty"..."Abu 'Ali went with the Imam into hiding"
- The succession of the Fatimd Imam al-Amir; by: S M Stern; p-206 Quote: "Other coins (Alexandria, 526)..read as follows: "Al-imam al-mahdi al-qa'im bi-amri-llah "(declaring Hafiz as Al-Imam)
- "The Dawoodi Bohras - Yemen". thedawoodibohras.com. Retrieved 2016-07-27.
- Maulaana, Abul Qaasim Tayyib (23 October 2008). "21st Fatimid Imam". Team Alavi. Archived from the original on 14 April 2017. Retrieved 14 April 2017.
- The Succession to the Fatimid Imam Amir, by S M Stern, DRILL, p.196,97
- http://ismaili.net/heritage/node/10675; Quote: ‘Anyhow, the chief guardian of Tayyib was Ibn Madyan, who is said to have hidden the minor Tayyib in a mosque called Masjid ar-Rahma. Makrizi tells that the infant son of al-Amir was carried in a basket after wrapping it up and covering it over with vegetables. Here in the mosque, a wet nurse cared for him’
- http://archnet.org/system/publications/contents/3039/original/DPT0868.pdf?1384770478., p.9, THE CULT OF ALID SAINTS IN THE FATIMID MONUMENTS OF CAIRO, PART II: THE MAUSOLEA , By :CAROLINE WILLIAMS, page ‘47
- The succession of the Fatimd Imam al-Amir; by: S M Stern;p.223,24,25
- The Ismaili..,Daftary, p.284, 285
- The succession of the Fatimd Imam al-Amir; by: S M Stern;p.228,9
- ; p. 378-79
- ; 12.0 The Fatimid Da'i Al-Mu'ayyad: His Life , by: Dr. Abbas Hamdani, University of Wisconsin, Milwaukee (U.S.A.); Quote; "in the time of al-Mustansir, to Egypt and joined the lsma'ili faith at the bidding of Sayyidna al-Mu'ayyad from whom they acquired much knowledge. Their names were Lam Nath (Abadullah) and Rup Nath (later called Mawla'i Nurad-Din). Both of them returned from Egypt to their native village, Daham Gam, where their tombs still exist near Aurangabad."
- ; Census of India, 1961: Rajasthan, India. Office of the Registrar General; 'Syedi Fakhruddin was the son of Tarmal, Vazir of king Sidhraj Jaysingh who ruled over Gujarat during the period 1094-1134 A.D. Tarmal had accepted the Islamic faith from the missionaries ( Moulai Abadullah) of the Imam al- Mustansir of the Fatimid dynasty which then ruled over a vast territory in western Asia and North Africa with capital as Cairo....'
- , p.41
- The Ismaili, their history and doctrine by Farhad Daftary
- Religion,learning and science by Young Lathan
- Medieval Islamic civilisation by Joseph w. Meri, Bacharach
- Sayyida Hurra: The Isma‘ili Sulayhid Queen of Yemenby Dr Farhad Daftary
- Uyun al-akhbar written by Syedna Idris on the history of the Ismaili community from its origins up to the 12th century CE. period of the Fatimid caliphs and then the Tayyibi Ismaili community in Yemen.