Saul fell on his own sword at Mount Gilboa (1 Sam 31:4)

1 Sam 1-7 focuses on Samuel.  This book relates that when Israel's leaders were unfaithful God raised up new leaders for the people. A priest named Eli had faithless and immoral sons.  Samuel was born to a woman named Hannah, who had long been childless, and Samuel became Eli's assistant.  One night God told Samuel that Eli's family would be condemned because of their corruption. Eli's sons were killed in battle and Eli himself fell and died when he heard of the defeat.  When Samuel grew older, he rallied the Israelites for victory against the Philistines.

1 Sam 8-15 centers on Saul.  When Samuel's own sons proved faithless, the people wanted a king to rule them.  Samuel anointed Saul to be the first king over Israel.  Saul led Israel to victory in battle, but he wrongly offered sacrifices and violated God's command by keeping booty from battle. Therefore, Samuel warned that the kingdom would be taken away from Saul.

1 Sam 16-31 describes David's relations with Saul. After Saul proved to be unfaithful, Samuel anointed the young David to be king. David won renown by defeating the Philistine giant, Goliath. When Saul became jealous and tried to kill him David fled.  David lived as an outlaw but refused to kill Saul.  In the end, Saul tried to consult the ghost of Samuel, and after being mortally wounded in battle, Saul fell on his own sword and died..

1 Sam 3 - Call of Samuel
1 Sam 9 - Saul chosen to be king
1 Sam 16:1-13 - David chosen to be king
1 Sam 17 - David and Goliath
1 Sam 31 - Death of Saul