I like the way the Warren Wiersbe said it:
If Judges is the book of "no king," then 1 Samuel is the book of "man's king." The people of Israel asked for a king and God gave them Saul, from the tribe of Benjamin, who turned out to be a tragic failure. But the Lord had prepared David for the throne, and 2 Samuel is the book of "God's king."
While tradition ascribes the authorship of the two books of Samuel to Samuel him self, he can't be the author since he dies in 1 Samuel 25. He could have only been the author of the first portion of first Samuel. While some consider Nathan and Gad (based on 1 Chronicles 29:29), the author is unknown.
The books of 1st and 2nd Samuel record events that took place 1105 B.C. to 971 B.C. This records 135 years of Israel's history. During these critical years, Israel is transformed from a loosely bound group of tribes to a nation under the kingship of David. They go from no king, no leadership and being influenced by the gods of the lands around them to a leader, a king that is a man after God's own heart, a man pointing them toward the Lord.
As we begin 1 Samuel we see that Israel is at a spiritual low point. The book of Judges offered hope that God would and could still work in the nation. But, everyone did what was right in the own eyes. The tribes were segregated, they weren't a nation. The book of Ruth shows us that God is always working. Even in this confused and lost nation, the Lord had men and women who held fast to Him.
In 1 Samuel we see God at work in His people. Yet, we see His people have their own plan; their own ideas. We can certainly learn from the mistakes that were made. As Christians in our world today, there are many relevant lessons for us.
 Wiersbe, W. W. (2001). Be successful (p. 13). Colorado Springs, CO: Victor/Cook Communications.
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