2 Samuel 1 - David receives word that Saul and his sons were killed. The man giving the news takes credit for killing Saul with the hopes that he might receive a reward from David. A lot of people appear to still believe that David wanted Saul dead. But David has this man executed and then composes a song of tribute to Saul and Jonathan. David always supported those that God placed in power.
2 Samuel 2 - David is anointed king over Judah while Saul's son, Ishbosheth is made king over Israel. The two kingdoms collide in battle and Israel is defeated. However, Joab's younger brother, Asahel, is killed by Abner and this will set up a revenge killing later.
2 Samuel 3 - As David's kingship grows in strength, Ishbosheth's is weakening. Abner abandons Ishbosheth and seeks to turn Israel over to David. However, Joab takes his vengeance out on Abner and murders him. David shows his remorse by singing a song of tribute to him.
2 Samuel 4 - Two servants to Ishbosheth murder him and take his head to David. Again, they make the same mistake of thinking David would be pleased. He isn't! He has these men executed and shows his sadness at another of Saul's sons having been killed.