From the Cathedral's website:
St Augustine, the first Archbishop of Canterbury, arrived on the coast of Kent as a missionary to England in 597 AD. He came from Rome, sent by Pope Gregory the Great. It is said that Gregory had been struck by the beauty of Angle slaves he saw for sale in the city market and despatched Augustine and some monks to convert them to Christianity. [I know it was a different time and people thought about slaves differently, but it still sounds bizarre to me.]
Augustine's original building lies beneath the floor of the nave– it was extensively rebuilt and enlarged by the Saxons, and the Cathedral was rebuilt completely by the Normans in 1070 following a major fire. There have been many additions to the building over the last nine hundred years, but parts of the quire and some of the windows and their stained glass date from the 12th century.By 1077, Archbishop Lanfranc had rebuilt it as a Norman church, described as "nearly perfect". A staircase and parts of the North Wall - in the area of the North West transept also called the Martyrdom - remain from that building.
Again from the Cathedral website:
The Nave
The Romanesque Nave was replaced in the 14th century by the one we see today. Its tall columns rise to meet in delicate vaulted arches and gilt roof bosses high over our heads. It is one of the most magnificent surviving examples of English Perpendicular Gothic, designed by Henry Yevele, the King’s Master mason.
The Quire
The Quire was rebuilt and extended after a disastrous fire in 1174 destroyed the earlier structure. Thomas Becket's shrine was placed in the Trinity Chapel in 1220, until it was destroyed in 1538 during the Reformation by order of Henry VIII. The Corona, built as a separate shrine for the a piece of Becket's skull, completes the eastern exterior of the Cathedral in a unique fashion. Beautiful stained glass windows illustrate miracles and stories associated with St Thomas.