Konrad I of Gà Âogów (; – 6 August 1273/74), a member of the Silesian Piasts, was Silesian duke of Gà Âogów from 1249/50 until his death.
Konrad was the fourth son of Henry II the Pious, Duke of Silesia and High Duke of Poland, and Anna, daughter of the Pà Âemyslid king Ottokar I of Bohemia. At the time of his father's death in the 1241 Battle of Legnica against the Golden Horde, he and his younger brother Wà Âadysà Âaw were placed under the guardianship of their eldest brother Duke Bolesà Âaw II Rogatka. After Henry's sudden death, the Silesian Piasts were not able to maintain their dominant position: Bolesà Âaw II tried to succeed his father on the Polish throne at Kraków, but eventually could not prevail against his Piast cousin Konrad I of Masovia.
In order to avoid further fragmentation of the paternal lands, the elder duke, with the approval of their mother, sent Konrad to study in Paris, where he was to be educated with the intention of becoming a priest in the future. However, in 1248, when the young man found out about the division of the family lands between his older brothers Bolesà Âaw II, ruling as a Duke of Legnica, and Henry III the White, Duke at Wrocà Âaw, he returned to the country and claimed his part of the Silesian inheritance. Soon a preliminary agreement was reached under which Konrad remained under the protection and care of his older brother, who gave him the title of co-ruler in Legnica.
Bolesà Âaw II (who wanted to get rid of him) still proposed Konrad for spiritual posts: first, as Provost of Gà Âogów Cathedral, and then Bishop of Passau in Bavaria. Though he had not reached the canonical age, he was elected by the Passau cathedral chapter to succeed the deposed bishop Rüdiger of Bergheim; however, without approval by the Roman Curia. Konrad, nevertheless, didn't have any intention of pursuing an ecclesiastical career. He never entered Passau and soon resumed his conflict with Bolesà Âaw II.
In June 1249 Konrad fled to Greater Poland, where he could count on the support of Duke Przemysà  I. In 1251 he campaigned Bolesà Âaw's ducal lands and he managed to conquer Bytom Odrzaà Âski. Konrad's bonds with the Piast dukes of Greater Poland were reinforced after his marriage with Przemysà  I's sister Salome. His other brother Henry III the White soon became another ally in the fight against Bolesà Âaw II. With the help of his new allies, and thanks to the revolt of the townspeople of Gà Âogów, the campaign against Bolesà Âaw II ended in complete success. The Duke of Legnica was forced to accept his defeat and give the Lower Silesian lands of Gà Âogów up to Krosno Odrzaà Âskie and à »agaà  to Konrad as a duchy in his own right.
Until the end of his life Konrad's relations with his brother Bolesà Âaw II remain strained. In 1257 Konrad made a dangerous move and kidnapped Bolesà Âaw from his residence in Legnica. The duke regained his freedom after a few months, but it is unknown at what price. It can be said that after that the duke never left Bolesà Âaw II a moment of happiness, but in 1271 the Duke of Legnica managed to regain the town of Bolesà Âawiec near the Bóbr river.
Around 1255, Konrad founded the collegiate church in Gà Âogów, Lower Silesia. By about 1300, sculpted figures of the duke and his wife, Salome, were installed around the choir area.
From about 1260 Konrad established closer contacts with the Kingdom of Bohemia and became involved in the expansionist politics of King Ottokar II. Also he promoted the colonization in his lands, mostly by German settlers. This was a decisive contribution to the institution of the Magdeburg town law in his Gà Âogów residence in 1253. In contrast to his brother Bolesà Âaw II, Konrad vigorously supported Bishop Thomas I of Wrocà Âaw in his defence of church rights. However, when the bishop died in 1268 Konrad began to violate the privileges conferred by him, which led to conflicts with the new Bishop Thomas II Zaremba.
At the end of his life he founded a church in Zielona Góra (now a Co-cathedral) dedicated to his grandmother, St. Hedwig of Silesia. The church was completed only twenty years after his death by his son and heir Henry III.
In 1249 Konrad contracted his first marriage to Salome (b. ca. 1225 - d. April 1267/74), daughter of Duke Wà Âadysà Âaw of Greater Poland. They had:
By 1271/74, Konrad married his second wife, Sophie (b. ca. 1259 - d. 24 August 1318), daughter of Dietrich the Wise, Margrave of Landsberg (second son of Henry III, Margrave of Meissen) and â according to some sources â widow of the last legitimate male member of the House of Hohenstaufen, Conradin, King of Sicily and Jerusalem. They had no children.