How far back do Chinese universities go? Europe has many universities founded in the Medieval period; in the United States, universities started to be founded almost as soon as English settlers arrived. China, however, I know very little about.

I do know that China has a millenia-long history of scholarship and science, but that is not the same as organizing academia into universities or university-like institutions.

When did "universities" in the modern sense (i.e., permanent institutions that gather scholars to conduct research and provide higher education to students) begin to be founded in China?
Western Style Chinese Academy

From Tongwen Guan 同文舘 wiki page


  Tongwen Guan (Chinese: 同文舘), or the School of Combined Learning was a government school for teaching Western languages (and later scientific subjects), founded at Beijing, China in 1862 during the late-Qing dynasty ... It became part of the Imperial Capital University (now Peking University) since 1902. ...

Government sponsored Chinese style academy

From Shang Xiang 上庠 wiki page


  Shang Xiang (Chinese: 上庠; pinyin: shàng xiáng; Wade–Giles: Shang Hsiang), was a school founded in the Yu Shun (虞舜) era in China. Shun (2257 BCE–2208 BCE), the Emperor of the Kingdom of Yu (虞, or 有虞/Youyu), founded two schools. One was Shang Xiang (shang (上), means up, high), and the other one was Xia Xiang (下庠, xia (下) means down, low).[1][2] Shang Xiang was a place to educate noble youth. Teachers at Shang Xiang were generally erudite, elder and noble persons.


From Taixue (太学) wiki page


  Taixue ... was the highest rank of educational establishment in Ancient China between the Han Dynasty and Sui Dynasty ... The first nationwide government school system in China was established in 3 CE under Emperor Ping of Han ...

Privately owned Chinese style academy

From Academies (Shuyuan書院) wiki page


  ... shuyuan were usually private establishments, ... The shuyuan originated in 725 ...


From China’s Ancient Academies-Academies Tours to China


  ... According to “Records of All Officials,” a volume of The New Chronicles of the Tang Dynasty, “in the sixth year of the Kaiyan Reign (AD 718) Qianyuan Academy changed its name to Lizheng Academy (Academy of Elegance and Rectitude), the newly created positions of supervisors and copy editors were filled and compiler-academicians became auxiliary-academician ...