If I were to give a theme to Proverbs, it would be three points about wisdom.
1. Recognize and acknowledge wisdom.
2. Pursue it
3. Cherish and cling to it.
Proverbs is another compilation of multiple authors. Solomon is responsible for most of it, but Agur, son of Jakeh, and King Lemuel are also responsible for some near the end of Proverbs. It has been suggested by some I have read that even these latter authors are actually Solomon creating under another name. You can dig into this and make up your own mind if you like.
Chapter 1 lists a summary of ideas that identify what is trying to be accomplished in these overall writings. There are a what I will call run away/stay away verses in 9-19 and verses 20-33 can be summarized by a call to acknowledge the cry of wisdom all around us or suffer the consequences.
Chapter 2 tells us that once we have acknowledged wisdom, we should pursue it like the priceless thing it is, and you will reap many, many more benefits including but not limited to "...wisdom will come into your heart and knowledge will be pleasant to your soul." (I have a note about verses 4 and 5 and how they seem so similar to Matthew 13:44, 45).
Chapters 3-9 visits and revisits themes of cherishing the teachings, commands, principles, and person of the Lord, the father, and wisdom, and it bounces back and forth between singing the joys and benefits of doing this versus the tragic consequences that will come from being seduced both literally and figuratively away from faithfulness. Chapter 9 does this the most explicitly stating outright the two sides that battle as folly and wisdom and scoffers or the wise. Wisdom and folly are both presented as women, but wisdom invites the simple to come in and genuinely be cared for and nourished, but folly shouts and seduces people to their own destruction.
Chapters 10-29 are collections of what most actually think of regarding proverbs. These are filled with either individual or groupings of individual proverbs that address any number of various topics with principles of wisdom and insight.
Chapter 30 is a combination of praise, prayer and proverbs and has Agur listed as its author.
Chapter 31 refers to King Lemuel as the author. He is teaching lessons learned from his mother. It starts with advice to him about how to be a good king and ends with the famous descriptions of "an excellent wife."