Meanwhile, in the South...
Sometime in the 2nd to the 3rd Century A.D., the Chams, a people who it is believed are descendants of Austronesians from Taiwan and Borneo which share a heritage with inhabitants of Polynesia, Micronesia, and other parts of what we consider Southeast Asia (but including Madagascar), formed a series of polities in what we now call South Vietnam.
Around the 4th Century A.D., the Champa state began to Indianized, adopting Indian cultural practices and religion (Hinduism) - you may recall that this was similar to the Khmer Kingdom up to the mid-12th Century. At least one ruler of the Champa state sailed to India in the 5th Century A.D. to bathe in the River Ganges.
(Early Cham States circa 400 A.D. -
Source)
The Champa Kingdom was considered among the significant kingdoms in Southeast Asia. In the 7th Century, Sui China invaded and destroyed the capital. The Champa Kingdom recovered, and between the 7th and 10th Century A.D. was considered a major naval power; its fleets controlled the spice trade between China, India, and Indonesia - which attracted the attention of Javanese kingdom, who invaded and held the coastland for approximately 25 years in the 8th Century.
The Champa Kingdom and culture was sufficiently individualized that it is considered differentiating from Đại Việt. There are a number of existing fortress and temple ruins (which, sadly, we did not see).
The 12th Century A.D. saw an invasion of the Champa Kingdom by the Khmer Empire which saw a brief occupation - but retaliation when in 1177 A.D. the Champas invaded the Khmer Empire and defeated them on the Tonlé Sap (which was commemorated at Bayon Wat, which we visited. At least one of the bas reliefs I took a
picture of recalls this battle. The Khmer Empire responded by re-invading the Champa Kingdom from 1190-1203 A.D., making the Champa kingdom a dependency for 30 years.
The 12 Century also saw the arrival of Islam, following the trade routes that lead Hinduism and Buddhism there.
Like the Đại Việt, the Champa kingdom faced an invasion by the Mongols of the Yuan Dynasty from 1283-1285 A.D.. Joining with the Đại Việt, they engaged in a guerrilla war and eventually repelled the Yuan. It was following this war that the retired emperor of the Đại Việt, Trần Nhân Tông, arranged for a marriage between his daughter and the prince of the Champa Kingdom. The marriage, in 1306 A.D., saw the transfer of two provinces from Champa to Đại Việt. The purpose was to provide peace between the two kingdoms. Of note, after this marriage from 1307 to 1401 A.D. there is no indigenous literature from the Champa Kingdom, which had a rich history from the 4th Century A.D. to 1307 in Sanskrit. Additionally, no new construction was started in Champa for any major project.

(Champa Kingdoms prior to 1306 A.D. - Source)
(Champa States post 1306 A.D. -
SourceWe will end the history of the South here as well, stopping a bit early as we did for the North. It is around the 14th Century that the two paths directly merge again.