The first thing one must remember when talking about Stephen Báthory is that in the Báthory family there are multiple members named Stephen. The first Stephen Báthory was a Hungarian noble who was a loyal follower of King John Zápolya of Hungry. In 1529, the elder Báthory was made governor of Transylvania.
The elder Báthory youngest son, Stephen Báthory was born in 1553 and would become king of Poland. Báthory was elected prince of Transylvania in 1571 to succedd John II. In 1574, he was elected to succeed Henry of Valois who returned to rule France as Henry III. There was a minority that voted for Maximilian II, who was also the Holy Roman Emperor.
After becoming king, he married Anna, who was the daugther of Sigismund II and gave Transylvania to his brother Chistopher Báthory. Stephen then tired to capture Danzig but the people there successfuly resisted the attack and he was forced to recognize them as a independent city state.
There were several other military campaigns with most of the led against Russia and Ivan Vasleivich. His troops had invaded Livonia and Dorpat. The most important battle took place at Vilnius and force the Russians to retreat further into the steppes. In 1582, Báthory made peace with Russia and retained most of Livonia and all of Polotsk.
Before his death in 1586, Báthory supported the Society of Jesus in Poland in an attempt to reform the country. When he died, Sigismund III was elected king.
Information for this node was taken from various web encyclopedias inclduing http://www.bartleby.com/65/st/StphnB.html and http://www.encyclopedia.com/html/S/StphnB1.asp