Xia Dynasty: Did Xia Dynasty ever exist?

Introduction
Xia Dynasty 2200-1600 B.C. lasted for 500 years, founded by legendary Yu the Great (大禹). This legendary kingdom was built within Shanxi province. Before Yu was an emperor, he worked in Henan province for Yao & Shun (尧帝 & 舜帝) emperors. They were all the descendants of Huang Emperor. 

Pre Xia Dynasty based on 3 legends

1. Legend of Huang Emperor - Father of Han Chinese
About 5,000 years ago, in Henan province which lies along Huang river, was seen many tribes mushroomed in that area. Of which, Hua Xia (华夏) and Miao tribes were the most powerful.

Hua Xia had a tribal leader called Huang Di (黄帝), who is exceptionally creative and capable.  Having invented boat and vehicle, dwelling houses, & costumes etc. , he also defeated the barbarian Miao tribal leader Chi You (蚩尤) to the South due to land dispute with the Hua Xia tribes.  Since then, he was elected as the "Emperor" - the leader among other alliance tribal leaders.  Huang Di - considered as the first Han ethnic emperor. Han Chinese often referred themselves as the descendant of Yan & Huang Emperors, or merely Huang Emperor (炎黄子孙 or 黄帝子孙). 

Based on another legend, you will find story about Huang and Yan were the earliest emperors and later fought in a war where Yan Emperor was killed and leaving Huang the only emperor.

2. Legend of Yu and Gun (father and son) - Stopping the flood
Yu the Great was handpicked by Yao emperor (尧帝) to become his successor due to his contribution to the tribes in Henan province, where the area was devastated by flood from Huang river. Yu actually continued his father's work, Gun (鯀) who was ordered by Yao to stop the flood but failed and later executed by Yao. 

3. Legend of Yao & Shun - Sage power transition & Rise of Xia
During Yao as the emperor, he had Shun as his assistant. Because Shun's diligence and capabilities, Yao offered his throne to Shun.  Due to Yu's massive contributions (stopping the flood and retreating ShanMiao tribe), Yao instructed Shun Emperor to offer his throne to Yu.  Yao, Shun and Yu are the descendants of Huang Emperor from separate bloodline.  In fact Yu is the uncle of Shun. This tradition of sage power transition (禅让制) only lasted until Xia Dynasty - when Yu the Great passed his throne to Bo Yi (伯益) - the son of Gao Yao (皋陶), but later killed by Yu's son Qi (启) where Xia Dynasty marks the end of sage power transition tradition and overtook by the first family control power transition (世袭制) until modern day. 

Fall of Xia Dynasty
The fall of the Xia is blamed on its last king, Jie (桀王), who is corrupt and a tyrant as recorded in the Bamboo Annals (竹书纪年).  The people rose up in rebellion under the leadership of Cheng Tang (成汤), and defeated King Jie of Xia in the Battle of Ming Tiao (鸣条之战).  Tang founded Shang Dynasty.

Although there were no archaeological excavation found for Xia Dynasty's artefact, while the Records of the Grand Historians written by ShiMaQian, 《史记》(Shiji) only closely matches the text recorded by ancient text character on Oracle bones for Shang Dynasty; there are too much discrepancies among all historian records about Xia Dynasty.  Xia Dynasty is somehow not considered the first dynasty officially, but a legend or myth instead.