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|Ab urbe condita||1785|
|Balinese saka calendar||953–954|
|English Regnal year||N/A|
|Chinese calendar||辛未年 (Metal Goat)|
3728 or 3668
— to —
壬申年 (Water Monkey)
3729 or 3669
|- Vikram Samvat||1088–1089|
|- Shaka Samvat||953–954|
|- Kali Yuga||4132–4133|
|Japanese calendar||Chōgen 5|
|Minguo calendar||880 before ROC|
|Seleucid era||1343/1344 AG|
|Thai solar calendar||1574–1575|
1158 or 777 or 5
— to —
1159 or 778 or 6
|Wikimedia Commons has media related to 1032.|
- Spring – Emperor Romanos III (Argyros) sends a Byzantine expeditionary army under General Michael Protospatharios, which includes Western auxiliaries and elite troops of Asia Minor, to reinforce the Byzantine position in Calabria (Southern Italy).
- September 6 – King Rudolph III dies without any heirs. He bequeaths his entire dominions to Emperor Conrad II (the Elder), dispatching to him the Holy Lance and ring of St. Maurice, symbols of Burgundian investiture.
- Odo II, count of Champagne, invades Burgundy and seizes most of the kingdom for himself. With the assistance of Humbert I of Savoy, Queen-dowager Ermengarde (Rudolph III's widow) flees to the safety of Zürich.
- Winter – Conrad II marches with his army into Champagne and devastes the land – forcing Odo II to sue for peace and swear to abandon Burgundy. The bishops prevent Conrad from seizing control of Burgundy.
- The first mention is made of Kursk, Russia, in the hagiography of Theodosius, who becomes a monk at the Kiev Caves Monastery (approximate date).
- October – Pope John XIX dies after an 8-year pontificate at Rome. He is succeeded by his nephew Benedict IX as the 145th pope of the Catholic Church, while (probably) still in his teens.
- February 16 – Ying Zong, Chinese emperor (d. 1067)
- September 3 – Go-Sanjō, Japanese emperor (d. 1073)
- September 14 – Dao Zong, Chinese emperor (d. 1101)
- Abe no Munetō, Japanese nobleman and samurai (d. 1108)
- Cheng Hao, Chinese neo-confucian philosopher (d. 1085)
- Donald III (the Fair), king of Scotland (approximate date)
- Ermengol III (or Armengol), count of Urgell (d. 1065)
- Gao, Chinese empress consort and regent (d. 1093)
- Gyrth Godwinson, English nobleman (approximated date)
- Hugh de Grandmesnil, Norman warrior and sheriff (d. 1098)
- Osbern FitzOsbern, bishop of Exeter (approximate date)
- Touzi Yiqing, Chinese Zen Buddhist monk (d. 1083)
- Vratislaus II (or Wratislaus), king of Bohemia (d. 1092)
- July 28 – Constance of Arles, French queen
- July 29 – Matilda of Swabia, German duchess
- September 6 – Rudolph III, king of Burgundy
- October 4 – Sancho VI, duke of Gascony
- Ahmad Maymandi, Ghaznavid vizier
- Arslan Yabgu, Turkic chieftain and ruler
- Bezprym (or Besfrim), duke of Poland
- Constantine Diogenes, Byzantine general
- Gille Coemgáin, king of Moray (Scotland)
- John XIX, pope of the Catholic Church
- Li, Chinese consort and concubine (b. 987)
- Li Deming, Chinese rebel leader (b. 981)
- Odo II, margrave of the Saxon Ostmark
- Otto Orseolo (or Ottone), doge of Venice
- C.W. Previté-Orton, The Early History of the House of Savoy, (Cambridge University Press, 1912), p. 30.