10 events the sources record for this year, grouped by region.
What happened
China (4)
At the urging of Li Shanchang and others, Zhu Yuanzhang was enthroned as Prince of Wu and established the hundred officials. (History of Ming (Mingshi), Annals 明史 卷1 至正二十四年)
Zhu Yuanzhang campaigned against Wuchang again; Chen Li surrendered, and Han, Mian, Jing and Yue all fell. (History of Ming (Mingshi), Annals 明史 卷1 至正二十四年)
Vice Military Commissioner Yesu and Chamsa Bulanxi meet and fight at Huanghou Dian; Bulanxi barely escapes (History of Yuan (Yuanshi), Annals 元史 卷46 順帝 1364年 4月)
In the second month Chen Youliang placed his elder brother Youcai and left vice-councillor Wang Zhongxin at Tanzhou; when the Prince of Wu reached Wuchang, Zhongxin came as reinforcement but was defeated and surrendered; the Prince of Wu gave him the post of vice-minister and had him keep guarding Tanzhou. (Xu Zizhi Tongjian (Continuation of the Comprehensive Mirror) 권217 二月 단락217.8.0)
Korean Peninsula (4)
When the enemy takes Hamju, the commander abandons his troops and flees; Han Bang-sin and Kim Gwi advance to Hwaju but are broken, and all the land north of Hwaju falls. (Goryeosa (History of Goryeo) 世家 卷40 恭愍 十三年)
Our army reaches Jeongju, and the enemy, which had camped at Tancheon of Suju, is defeated, burns its camps, crosses the river and flees. (Goryeosa (History of Goryeo) 世家 卷40 恭愍 十三年)
January 1364: Choe Yu, with 10,000 Yuan troops, escorts Prince Deokheung across the Amnok River and besieges Uiju. An U-gyeong repels them in seven battles, but military commissioner Hong Seon is captured and Goryeo forces are defeated and fall back to Anju. Choe Yeong is rushed in as commander (Goryeosa Jeolyo (Essentials of Goryeo History) 권28 恭愍王 十三年)
1364: Jurchen Samseon, Samgae and others take Hamju; the chiefs Jeon I-do and Yi Hui abandon their troops and flee. Yi Seong-gye was away relieving the northwest (Goryeosa Jeolyo (Essentials of Goryeo History) 권28 恭愍王 十三年)
Southeast Asia (2)
Gajah Mada (Mahapati) passed away, and the king grieved deeply. (Nagarakretagama raw 줄 2382, 필사 쪽 (123a))
To succeed Gajah Mada, senior ministers were chosen: Pu Tandi (atmaraja), Pu Nala (mandalika) and others. (Nagarakretagama raw 줄 2403, 필사 쪽 (123b))