Conrad besieges and takes Capua and gives…

The Tangut tribe, who speak a now-extinct Qiangic language (Tibeto-Burman), which is distantly related to Chinese, had moved from place to place and eventually settled in northwestern China (Ningxia, Gansu, and Shaanxi).

From the moment they entered this region they had undergone a process of sinicization.

Eventually, the Tangut state had been founded in the year 1031 by Li Deming.

Known in the Chinese language as "Xi-Xia", the Tangut people call their state "phiow-bjij-lhjij-lhjij", which translates to "The Great State of Whiteness and Loftiness."

Yeli Renrong, is a scholar close to the Tangut Emperor Li Yuanhao, who, according to the official History of Song, commanded him to design the complex Tangut script in 1036 or 1038, based on Chinese writing, for use in writing the Tangut language.

King Stephen of Hungary has established church institutions, replaced tribal land systems with individual proprietorship, and extended Hungarian political influence to the foothills of the Carpathians.

As his only son, Emeric, had died in a hunting accident in 1031 and he has exiled his closer Árpád relatives for their unwillingness to renounce their pagan faith, he designates as his successor his distant relative Pietro Orseolo, who was born on in Venice as the only son of Doge Otto Orseolo; his mother is a sister of Stephen.

After the Venetians rose up and deposed Otto in 1026, Peter had not followed his father in flight to Constantinople.

He instead went to Hungary, where his uncle had appointed him commander of the royal army.

Stephen's cousin Vazul had had the strongest claim to the throne, but the king had overlooked him and named Peter as his heir.

Vazul had been blinded shortly thereafter and his three sons—Levente, Andrew and Béla—exiled, which has strengthened Peter's right of succession.

The king has asked Peter to take an oath respecting the property of his wife, Queen Giselle, suggesting that Peter's relationship with his aunt was tense.

Stephen dies on August 15, 1038.

Peter succeeds him and adopts an active foreign policy.

John puts Stephen in charge of the fleet bearing George Maniakes and his army to Sicily in 1038.

The Ghaznavid ruler Mahmud had deposed ithe Buyid emir Majd al-Dawla had in 1029.

Mas'ud I, the son of the Ghaznavid sultan, who wishes to liberate the Abbasids from Buyid control, had proceeded further into western Iran, where he had defeated various rulers, including Muhammad, who had fled to Ahvaz to seek help from the Buyids, but he had quickly made peace with the Ghaznavids and returned as their vassal, having accepted to pay an annual tribute of two hundred thousand dinars.

The Ghaznavids, however, are not able to control those of their conquests that are distant from Ghazni, without trouble.

Muhammad had managed to briefly take Ray from the Ghaznavids in 1030.

In 1035, Mas'ud I again defeats Muhammad, who fled to once again fled to the Buyids in Ahvaz, whence he later flees to northwestern Iran to begin recruiting a powerful force of Turkmens in order to gain his lost regions.

Muhammad, along with his forces, once again occupies Rey in 1037 and 1038.

Shibl al-Daula Nasr, Amir of Aleppo, had eventually transferred his allegiance from Constantinople to the Fatimids.

However, Nasr, like his father is killed fighting al-Duzbari as well, in 1038.

Nasr’s brother Thimal flees, together with his Numayrid ally Shabib ibn Waththab, back to Aleppo.

Al-Duzbari advances on the town, however, and is received in a friendly manner by the citizenry, who are upset of the Mirdasids' alignment with the Constantinople.

Thimal had already retreated from Aleppo; his cousin Mukallad b. Kamil b. Mirdas, who had been in charge of the citadel, is allowed to depart peacefully.

Prince Guaimar IV of Salerno requests in 1038 that Emperor Conrad II adjudicate in a dispute over Capua with its Prince Pandulf, whom Conrad had released from imprisonment in 1024, immediately after his coronation.

Hearing that Michael IV, Emperor in Constantinople, had received the same request, Conrad goes to southern Italy, to Salerno and Aversa.

Conrad appoints Richer, from Germany, as abbot of Monte Cassino, the abbot Theobald being imprisoned by Pandulf.

At Troia, Conrad orders Pandulf to restore stolen property to Monte Cassino.

Pandulf sends his wife and son to ask for peace, giving three hundred pounds of gold and a son and daughter as hostages.

The Emperor accepts Pandulf's offer, but the hostages escape and …

…Pandulf holes up in his outlying castle of Sant'Agata de' Goti.

Harald Hardrada joins the imperial forces in 1038 in George Maniakes's (the sagas' "Gyrge") attempt to reconquer Sicily from the Saracens, who had established an emirate on the island.

During the campaign, Harald fights alongside Norman mercenaries such as William Iron Arm.

According to Snorri Sturluson, Harald captured four towns on Sicily.