The Chinese Dynasty's consisted of three individual dynasty's. They were the Sui, Tang, and Song Dynasty's.
The Sui Dynasty~
First off was the Sui Dynasty. They ruled from roughly 589 A.D - 618 A.D. The first emperor of Sui was Emperor Wendi. Then after Wendi's time was done, Yang Di took over Sui. Luoyang was the Dynasty's first capital. One of the Sui's greatest achievements was the building of the Grand Canal. This was very important to the dynasty's economic growth because it really increased trade between the Dynasty and bordering traders and such.
The Tang Dynasty~
The Tang Dynasty was the dynasty that followed the Sui Dynasty. And in a way, the Tang Dynasty was a lot like the Han Dynasty in that they both arose from the swirling chaos and brought peace and order to the community. There were many, many, many rulers of the Tang Dynasty. Three pretty popular ones are, in order of rule, Taizong, Empress Wu Zhao, and Xuanzong. The Capital of the Tang Dynasty was Chang'an. Just like the number of emperors in the Tang Dynasty, achievements of the Tang Dynasty were plentiful. But to just name a few... there was advances in medicine, creation of gunpowder, and the study of law and math. But even with all those achievements the dynasty fell hard. The biggest cause of this was peasant uprising. Which ultimately brought Tang to its knees.
The Song Dynasty lasted from 960 to 1279. The Song Dynasty was split into a Northern and Southern Song Dynasty. The First ruler of the Northern Song was Zhao Kuangyin. Where as the founder of the Southern Song was Zhao Gou who was the youngest son of the ruler of Northern Song. And the capital that Northern Song established was Bianjing, current day Kaifeng. Southern Song however made their capital Lin'an. Achievements of the Northern Song Dynasty were advances in literature and the arts. Southern achievements were in pottery and arts.