Short answers, pulled from the story.
Liu Bang founded the Han dynasty in 202 BC after defeating his rival Xiang Yu at the Battle of Gaixia. He assumed the title of Emperor Gaozu and established the capital at Chang'an, modern-day Xi'an.
Emperor Wu launched massive invasions starting in 133 BC that culminated in the Battle of Mobei in 119 BC. Commanders Huo Qubing and Wei Qing forced the Xiongnu court to flee north of the Gobi Desert.
Wang Mang seized power on the 10th of January 9 AD and his regime fell due to massive floods of 11 AD and 12 AD. These floods dislodged thousands of peasant farmers who joined rebel groups like the Red Eyebrows to survive.
The Han dynasty ended in 220 AD when Cao Pi usurped the throne from Emperor Xian. This event formally initiated an age of conflict between the Three Kingdoms: Cao Wei, Eastern Wu, and Shu Han.
Cai Lun invented the standard papermaking process in 105 AD and the oldest known surviving piece of paper dates to 110 AD. The dynasty also saw the invention of the three-legged iron seed drill and the heavy mouldboard iron plough.
Emperor Wu gave Confucianism exclusive patronage in 136 BC and abolished all academic chairs not concerned with the Five Classics. He established the Imperial University in 124 BC where nominees for office received a Confucian education.