I started Uriel Simon's Four Approaches to the Book of Psalms: From Saadiah Gaon to Abraham Ibn Ezra. This book is about medieval Jewish opinions on the Book of Psalms. A professor recommended it to me in 2006, and I've finally gotten around to reading it! I do not remember what the professor's exact point was in recommending this book to me. I think he was making the point that Judaism has not regarded the Writings (i.e., Psalms, Proverbs, Ecclesiastes, Song of Solomon, Job, Daniel, Lamentations) as authoritative to the same extent as the Torah, or as verbally inspired. I asked the professor how, if that were the case, rabbinic literature made verbal links between words in the Torah and words in the Writings. Essentially, rabbis would see a word in the Torah, then they would look for how that word was used elsewhere in the Hebrew Bible, and they would interpret that word in the Torah in light of what it means in other places. Wasn't the presupposition behind this exercise that God was the author of the entire Hebrew Bible---that God had inspired both the Torah and also the rest of the Hebrew Bible, even at the verbal level? My professor responded that there have been different views within Judaism on the Writings, and he recommended to me Uriel Simon's work.
So far, I have read Chapters 1 and 2. Chapter 1 is about Saadiah Gaon, and his view was that the Psalms were God's word to human beings (through an angelic intermediary) rather than human beings' words to God (prayer). Saadiah regarded the Book of Psalms as like a second Pentateuch, which contained God's exhortations and instructions to human beings. Chapter 2 was about some Karaites, who regarded the Book of Psalms as a collection of prophetic prayers that were made under the inspiration of the Holy Spirit. In the same way that Hannah's song in I Samuel 2 was Hannah's speech to God and yet predicted the future (i.e., God overthrowing oppressors) in a prophetic sense, so also could the Book of Psalms contain prayers that were from human beings to God and yet predicted future events under divine inspiration. According to the Karaites, the Psalms flowed from the personal circumstances of various Psalmists, but they were also adaptable to the future experiences and trials of the Jews (such as the Karaites), plus they predicted the Messiah. For the Karaites, this was because the Psalms were prophetic.
I think that this book could be of interest to Christians, for it is about how thinkers have wrestled with how to categorize the Book of Psalms. Are the Psalms God's words to human beings, human beings' words to God, or both? People of faith have said that not everything that the Psalmist speaks in the Psalms is from the mouth of God---for example, God does not want us to wish harm on our enemies. We are to regard these words as the expressions of the Psalmist's heart. And yet, in the New Testament, the Psalms were regarded as prophetic about Jesus Christ, which entails divine inspiration.
This book contains other interesting elements as well. For example, in my reading today, I learned that Saadiah Gaon used the Book of Daniel to predict the date of the Messiah's coming, which rabbinic Judaism had frowned upon. Saadiah said that the Messiah would come in 968 C.E., but Saadiah was dead by then. Jewish thinkers criticized Saadiah for this, especially after his prediction failed to come to pass. But Maimonides had some sympathy for Saadiah, for Maimonides thought that Saadiah was giving the Jewish people hope when they needed it.