Note that much of the detail in the chart below is apocryphal or speculative. The dates of Shankara's life are not known with any certainty. Most authorities seem to agree today that he lived in the 9th Century AD but some still claim the 5th century BC. He is traditionally supposed to have founded four 'mathas' (monasteries) in different parts of India to keep the tradition alive and provide centres where seekers could find true teachers of Advaita. These were Sringeri Math at Karnataka in the South (Bhurivara sampradaya or sect), Dvaraka Math at Gujurat in the West (Keeravara sampradaya), Puri Math at Orissa in the East (Bhagavara sampradaya) and Jyotirmath at Uttaranchal in the North (Anandavara sampradaya). According to Wikipedia, however, there is no evidence for the existence of any of them prior to the 14th Century. The matha at Kanchipuram also claims to be have been founded by Shankara and the Kanchi Kamakoti organisation has what is purported to be a record of all of the Shankaracharyas stretching back to Adi Shankara in 482 BC, followed by his main disciple Suresvara. Sringeri also claims Suresvara as its initial Shankaracharya, though uses the date of AD 820 for its founding. See Wikipedia for general information on Shankara and links to related sites.
Details of Shankara's disciples may be found here.