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|Ab urbe condita||2131|
|Balinese saka calendar||1299–1300|
|English Regnal year||1 Ric. 2 – 2 Ric. 2|
|Chinese calendar||丁巳年 (Fire Snake)|
4074 or 4014
— to —
戊午年 (Earth Horse)
4075 or 4015
|- Vikram Samvat||1434–1435|
|- Shaka Samvat||1299–1300|
|- Kali Yuga||4478–4479|
|Japanese calendar||Eiwa 4|
|Minguo calendar||534 before ROC|
|Thai solar calendar||1920–1921|
1504 or 1123 or 351
— to —
1505 or 1124 or 352
|Wikimedia Commons has media related to 1378.|
- March – In England, John Wycliffe tries to promote his ideas for Catholic reform by laying his theses before Parliament, and making them public in a tract. He is subsequently summoned before the Archbishop of Canterbury, Simon of Sudbury, at the episcopal palace at Lambeth, to defend his actions.
- April 9 – Following the death of Pope Gregory XI, and riots in Rome calling for a Roman pope, the cardinals, who are mostly French, elect Pope Urban VI (Bartolomeo Prignano, Archbishop of Bari) as the 202nd Pope.
- July – Revolt of the Ciompi: Discontented wool carders briefly take over the government of Florence.
- August 4 – Gian Galeazzo Visconti succeeds his father, Galeazzo II Visconti, as ruler of Milan.
- September – A contract is set up between Richard le Scrope, 1st Baron Scrope of Bolton and the mason Johan Lewyn, for the construction of Bolton Castle.
- September 20 – Unhappy with Pope Urban's critical attitude towards them, the majority of the cardinals meet at Fondi, elect Clement VII as antipope, and establish a rival papal court at Avignon. This split within the Catholic Church becomes known as the Western Schism.
- November 10 – Estimated appearance date of Halley's Comet.
- November 29 – Charles IV, Holy Roman Emperor, dies in Prague. He is succeeded by his son, Wenceslaus, as King of Bohemia, but the office of Holy Roman Emperor falls into abeyance, until Charles's son Sigismund is crowned in 1433.
- Holy Roman Emperor Charles IV visits his nephew Charles V of France, to publicly celebrate the friendship between their two nations.
- France, Aragon, Castile and León, Cyprus, Burgundy, Savoy, Naples and Scotland choose to recognise Antipope Clement VII. Denmark, England, Flanders, the Holy Roman Empire, Hungary, northern Italy, Ireland, Norway, Poland and Sweden continue to recognise Pope Urban VI.
- Dmitri Donskoi of Moscow & Vladimir resists a small invasion, by the Mongol Blue Horde.
- Tokhtamysh dethrones Timur Malik, as Khan of the White Horde.
- Kara Osman establishes the Turkomans of the White Sheep Dynasty at Diyarbakır, in present-day southeast Turkey.
- The Turks capture the town of Ihtiman, in west Bulgaria.
- Uskhal Khan succeeds his father, Biligtü Khan, as ruler of the Yuan Dynasty in Mongolia.
- Balša II succeeds his father, Durađ I, as ruler of Zeta (now Montenegro).
- Tai Bian succeeds Zhao Bing Fa, as King of Mong Mao (now northern Myanmar).
- Da'ud Shah succeeds his assassinated nephew, Aladdin Mujahid Shah, as Bahmani Sultan in present-day southern India. Da'ud Shah is assassinated in the same year, and is succeeded by Mohammed Shah II.
- Sa'im al-Dahr is hanged, for blowing the nose off the Sphinx.
- January 23 – Louis III, Elector Palatine (d. 1436)
- May 27 – Zhu Quan, Chinese military commander, historian and playwright (d. 1448)
- August 16 – Hongxi Emperor of China (d. 1425)
- October 24 – David Stewart, Duke of Rothesay (d. 1402)
- December 31 – Pope Callixtus III (d. 1458)
- date unknown
- February 6 – Joanna of Bourbon, queen of Charles V of France (b. 1338)
- March 27 – Pope Gregory XI
- July – Owain Lawgoch, titular Prince of Wales – assassinated (b. c. 1330)
- August 4 – Galeazzo II Visconti, Lord of Milan (b. c. 1320)
- November 29 – Charles IV, Holy Roman Emperor (b. 1316)
- November 30 – Andrew Stratford, English verderer and landowner