Taxi: Getting from the airport to Peking University (please refer to the website http://map.pku.edu.cn/ for a map of Peking University) by taxi would normally take 40 – 50 minutes, and cost about 110 – 140 RMB, depending on your arrival terminal.
Airport Shuttle Bus: The Airport Shuttle Bus (Zhongguancun (中关村) Line) has a stop outside the East Gate of Peking University (北京大学东门站), and costs 24 RMB. It runs from 06:50 to 01:00 (the next day), every 30 minutes.
Subway: The subway is recommended if you do not have too much luggage and arrive between 6:30 and 21:30. Take the line Airport Express (机场快线) from Terminal 2 or Terminal 3, change to Line 10 at the Sanyuanqiao (三元桥) station, then transfer to Line 4 at Haidian Huangzhuang (海淀黄庄) station, and finally get off at the East Gate of Peking University (北大东门) station, Exit C. The Airport Express fare is 25 RMB; the subway fare from 三元桥 to 北大东门 is 5 RMB. The total journey time is about 55 minutes.
Useful Links:
Route map of Beijing Subway: https://www.bjsubway.com/jpg.html
Map of PKU: https://maps.pku.edu.cn/index_en.html
Beijing Capital International Airport: http://www.bcia.com.cn/