Question: Who was the second wife Sigismund I the Old, the King of Poland and Grand Duke of Lithuania and mother of Anna Jagiellon?

Context articles: Alexander Jagiellon
Lithuanian Civil War (1389–92)
Anna Jagiellon
Sophia of Halshany
Bona Sforza
Sigismund I the Old
War of the Polish Succession (1587–88)
Stephen Báthory
Aleksander Chodkiewicz
Andrei of Polotsk

Alexander I Jagiellon (Polish: "Aleksander Jagiellończyk" ; Lithuanian: "Aleksandras Jogailaitis" ) (5 August 1461 – 19 August 1506) of the House of Jagiellon was the Grand Duke of Lithuania and later also King of Poland.
 He was the fourth son of Casimir IV Jagiellon.
 He was elected Grand Duke of Lithuania on the death of his father (1492), and King of Poland on the death of his brother John I Albert (1501).
The Lithuanian Civil War of 1389–92 was the second civil conflict between Jogaila, King of Poland and Grand Duke of Lithuania, and his cousin Vytautas.
 At issue was control of the Grand Duchy of Lithuania, then the largest state in Europe.
 Jogaila had been crowned King of Poland in 1386; he installed his brother Skirgaila as ruler of Lithuania.
 Skirgaila proved unpopular and Vytautas attempted to depose him.
 When his first attempt to take the capital city of Vilnius failed, Vytautas forged an alliance with the Teutonic Knights, their common enemy – just as both cousins had done during the Lithuanian Civil War between 1381 and 1384.
 Vytautas and the Knights unsuccessfully besieged Vilnius in 1390.
 Over the next two years it became clear that neither side could achieve a quick victory, and Jogaila proposed a compromise: Vytautas would become Grand Duke and Jogaila would remain Superior Duke.
 This proposal was formalized in the Ostrów Agreement of 1392, and Vytautas turned against the Knights.
 He went on to reign as Grand Duke of Lithuania for 38 years, and the cousins remained at peace.
Anna Jagiellon (Polish: "Anna Jagiellonka" , Lithuanian: "Ona Jogailaitė" ; 18 October 1523 – 12 November 1596) was Queen of Poland and Grand Duchess of Lithuania in her own right from 1575 to 1586.
 She was a daughter of Polish King Sigismund I the Old and his Italian wife Bona Sforza.
 Despite multiple proposals, she remained unmarried until the age of 52.
 After the death of King Sigismund II Augustus, her brother and the last male member of the Jagiellon dynasty, Anna's hand was sought by pretenders to the Polish–Lithuanian throne to maintain the dynastic tradition.
 She was elected, along with her then-fiancé Stephen Báthory, as co-ruler in the 1576 royal election of the Polish–Lithuanian Commonwealth.
 Their marriage was a formal arrangement and distant.
 Báthory was preoccupied with the Livonian War, while Anna spent her time in Warsaw on local administrative matters and several construction works.
 After Báthory's death in December 1586, she had an opportunity to claim the throne for herself (she was co-ruler and not merely a consort), but did not even attempt it.
 Instead, she promoted her nephew Sigismund III Vasa, establishing House of Vasa on the Polish–Lithuanian throne for the next eighty years (1587–1668).
Sophia of Halshany or Sonka Olshanskaya (Belarusian: Соф'я Гальшанская, "Sofja Halšanskaja" ; Lithuanian: "Sofija Alšėniškė" ; Polish: "Zofia Holszańska" ;  1405 – September 21, 1461 in Kraków) was a Grand Duchy of Lithuania princess of Halshany.
 As the fourth and last wife of Jogaila, King of Poland and Supreme Duke of Lithuania, she was Queen consort of Poland (1422–1434).
 As the mother of Władysław III, King of Poland and Hungary, and Casimir IV, Grand Duke of Lithuania and King of Poland, she was the founder of the Jagiellon dynasty.
Bona Sforza (2 February 1494 – 19 November 1557) was a member of the powerful House of Sforza, which ruled the Duchy of Milan since 1447.
 In 1518, she became the second wife of Sigismund I the Old, the King of Poland and Grand Duke of Lithuania.
 Their marriage lasted 30 years until Sigismund's death in 1548.
 Ambitious and energetic, Bona became heavily involved in the political life of Poland–Lithuania.
 To increase state revenue, she implemented various economic and agricultural reforms, including the far-reaching Wallach Reform in the Grand Duchy of Lithuania.
 Her reforms made her the richest landowner in the Grand Duchy.
 In foreign policy, she opposed the Habsburgs and sought to secure her eldest daughter Isabella Jagiellon in the Kingdom of Hungary.
Sigismund I of Poland (Polish: "Zygmunt I Stary" , Lithuanian: "Žygimantas I Senasis" ; 1 January 1467 – 1 April 1548), of the Jagiellon dynasty, reigned as King of Poland and also as the Grand Duke of Lithuania from 1506 until 1548.
 Earlier, Sigismund had been invested as Duke of Silesia.
 A successful monarch and a great patron of arts, he established Polish suzerainty over Ducal Prussia (East Prussia) and incorporated the duchy of Mazovia into the Polish state, securing the nation's wealth, culture and power.
The War of the Polish Succession or the Habsburg-Polish War took place from 1587 to 1588 over the election of monarch after the death of King of Poland and Grand Duke of Lithuania Stephen Báthory.
 The war was fought between factions of Sigismund III Vasa and Maximilian III, with Sigismund eventually being crowned King of Poland and Grand Duke of Lithuania.
 Two major battles of this conflict included the Siege of Kraków, in which Maximilian III failed to capture the capital of the Commonwealth, and the Battle of Byczyna, in which Maximilian was forced to surrender.
 Sigismund's victory was significantly the doing of Chancellor and Hetman Jan Zamoyski, who stood behind both the political intrigue and the military victories of this conflict.
Stephen Báthory (Hungarian: "Báthory István" ; Polish: "Stefan Batory" ; Belarusian: Стэфан Баторы ; Lithuanian: "Steponas Batoras" ; Romanian: "Ștefan Báthory" ; 27 September 1533 – 12 December 1586) was Voivode of Transylvania (1571–76), Prince of Transylvania (1576–86), from 1576 Queen Anna Jagiellon's husband and "jure uxoris" King of Poland and Grand Duke of Lithuania (1576-1586).
Aleksander Chodkiewicz (Lithuanian: "Aleksandras Chodkevičius" , Belarusian: Аляксандар Хадкевіч ; ca. 1475 – 28 May 1549) was a noble from the Grand Duchy of Lithuania, founder of the Supraśl Orthodox Monastery.
 He inherited vast possessions from his father Ivan Chodkiewicz, which made him 11th wealthiest person in the Grand Duchy according to the military census of 1528.
 Via his mother Jawnuta (Agnieszka) of the Belsky family, he was second cousin to Kings of Poland John I Albert, Alexander Jagiellon, and Sigismund I the Old.
 Chodkiewicz quickly gained influence under Alexander Jagiellon, becoming royal marshal.
 However, after Alexander's's death in 1506 his career stagnated.
 He supported Queen Bona Sforza, gaining her favor and becoming starost of Brest in 1528.
 The peak of his career came in 1544 when young Sigismund II Augustus, still influenced by his mother, appointed Chodkiewicz as voivode of Nowogródek and his son Hieronim as castellan of Trakai.
Andrei of Polotsk (Belarusian: Андрэй Альгердавіч , Lithuanian: "Andrius Algirdaitis" Polish: "Andrzej Olgierdowic" , ca. 1325 – 12 August 1399, in the Battle of the Vorskla River) was the eldest son of Algirdas, Grand Duke of Lithuania, and his first wife Maria of Vitebsk.
 He was Duke of Pskov (through his deputy Yuri, 1342–1348) and Polotsk (1342–1387).
 As the eldest son of the Grand Duke, Andrei claimed his right to the throne after his father's death in 1377.
 Algirdas left Jogaila, his eldest son with his second wife Uliana of Tver, as the rightful heir.
 Andrei's rivalry with Jogaila, Grand Duke of Lithuania and later King of Poland, eventually led to his demise.