Jerusalemites, Levitical Responsibilities and the Family of Saul
The reference to the "book of the kings of Israel" in verse 1 is evidently not to the biblical books of Kings, as these contain no genealogies.
Expositor's comments in its introduction to this chapter: "Chapter 9 itself is sometimes assigned to the period of Persian restoration…or even equated with a list of Nehemiah's during his own time (444 B.C.), of those who lived in Jerusalem and of those who resided outside (Nehemiah 11:3-24 Nehemiah 11:3-24  Now these are the chief of the province that dwelled in Jerusalem: but in the cities of Judah dwelled every one in his possession in their cities, to wit, Israel, the priests, and the Levites, and the Nethinims, and the children of Solomon's servants.
 And at Jerusalem dwelled certain of the children of Judah, and of the children of Benjamin. Of the children of Judah; Athaiah the son of Uzziah, the son of Zechariah, the son of Amariah, the son of Shephatiah, the son of Mahalaleel, of the children of Perez;
 And Maaseiah the son of Baruch, the son of Colhozeh, the son of Hazaiah, the son of Adaiah, the son of Joiarib, the son of Zechariah, the son of Shiloni.
 All the sons of Perez that dwelled at Jerusalem were four hundred three score and eight valiant men.
 And these are the sons of Benjamin; Sallu the son of Meshullam, the son of Joed, the son of Pedaiah, the son of Kolaiah, the son of Maaseiah, the son of Ithiel, the son of Jesaiah.
 And after him Gabbai, Sallai, nine hundred twenty and eight.
 And Joel the son of Zichri was their overseer: and Judah the son of Senuah was second over the city.
 Of the priests: Jedaiah the son of Joiarib, Jachin.
 Seraiah the son of Hilkiah, the son of Meshullam, the son of Zadok, the son of Meraioth, the son of Ahitub, was the ruler of the house of God.
 And their brothers that did the work of the house were eight hundred twenty and two: and Adaiah the son of Jeroham, the son of Pelaliah, the son of Amzi, the son of Zechariah, the son of Pashur, the son of Malchiah.
 And his brothers, chief of the fathers, two hundred forty and two: and Amashai the son of Azareel, the son of Ahasai, the son of Meshillemoth, the son of Immer,
 And their brothers, mighty men of valor, an hundred twenty and eight: and their overseer was Zabdiel, the son of one of the great men.
 Also of the Levites: Shemaiah the son of Hashub, the son of Azrikam, the son of Hashabiah, the son of Bunni;
 And Shabbethai and Jozabad, of the chief of the Levites, had the oversight of the outward business of the house of God.
 And Mattaniah the son of Micha, the son of Zabdi, the son of Asaph, was the principal to begin the thanksgiving in prayer: and Bakbukiah the second among his brothers, and Abda the son of Shammua, the son of Galal, the son of Jeduthun.
 All the Levites in the holy city were two hundred fourscore and four.
 Moreover the porters, Akkub, Talmon, and their brothers that kept the gates, were an hundred seventy and two.
 And the residue of Israel, of the priests, and the Levites, were in all the cities of Judah, every one in his inheritance.
 But the Nethinims dwelled in Ophel: and Ziha and Gispa were over the Nethinims.
 The overseer also of the Levites at Jerusalem was Uzzi the son of Bani, the son of Hashabiah, the son of Mattaniah, the son of Micha. Of the sons of Asaph, the singers were over the business of the house of God.
 For it was the king's commandment concerning them, that a certain portion should be for the singers, due for every day.
 And Pethahiah the son of Meshezabeel, of the children of Zerah the son of Judah, was at the king's hand in all matters concerning the people.
American King James Version×). But while this latter document exhibits the same order in its categories (perhaps because based on 1 Chron 9), caution is advised. Thus [as one scholar] admits: 'The two lists are not so alike as sometimes supposed...' The M[asoretic] T[ext] has about eighty-one names for Nehemiah 11 and about seventy-one for Chronicles, of which only about thirty-five are the same or nearly so. Moreover some of these have a permanent relevance, e.g., names of priestly courses (vv. 10, 12) or of genealogical ancestors (vv. 11, 16), which are not subject to change in any event."
In other words, it is not clear whether the list of people dwelling in Jerusalem in verses 3-9 predates or postdates the Babylonian Exile. Some suggest that the reason for highlighting the inhabitants of Jerusalem is to put the focus on the city of David in contrast to Saul's city of Gibeon in the previous chapter. "While both cities were important centers, God had not chosen Gibeon. But He did choose Jerusalem, not [merely] as Israel's political capital but as the location for His temple. It was in Jerusalem, where the ark [i.e., the Ark of the Covenant] rested, that God met with His people. It was Jerusalem where the priests offered sacrifices for sin. It was Jerusalem where the Levites led in worship" (Bible Reader's Companion, note on 8:1-9:44).
Jerusalem is "the apple of God's eye" (Zechariah 2:8 Zechariah 2:8For thus said the LORD of hosts; After the glory has he sent me to the nations which spoiled you: for he that touches you touches the apple of his eye.
American King James Version×). Beyond the focus of 1 Chronicles 9, the place had been special to God even long before the children of Israel dwelt there. Mount Moriah, the Temple Mount in Jerusalem, had been the place God sent Abraham for the test with Isaac (Genesis 22:2 Genesis 22:2And he said, Take now your son, your only son Isaac, whom you love, and get you into the land of Moriah; and offer him there for a burnt offering on one of the mountains which I will tell you of.
American King James Version×). Indeed, Jerusalem was the site chosen by God for the sacrifice of Jesus Christ, and it will be the city from which God will later rule the world and even the universe.
Finally, verses 35-44 present again the family of Saul, basically repeating 1 Chronicles 8:29-38 1 Chronicles 8:29-38  And at Gibeon dwelled the father of Gibeon; whose wife's name was Maachah:
 And his firstborn son Abdon, and Zur, and Kish, and Baal, and Nadab,
 And Gedor, and Ahio, and Zacher.
 And Mikloth begat Shimeah. And these also dwelled with their brothers in Jerusalem, over against them.
 And Ner begat Kish, and Kish begat Saul, and Saul begat Jonathan, and Malchishua, and Abinadab, and Eshbaal.
 And the son of Jonathan was Meribbaal; and Meribbaal begat Micah.
 And the sons of Micah were, Pithon, and Melech, and Tarea, and Ahaz.
 And Ahaz begat Jehoadah; and Jehoadah begat Alemeth, and Azmaveth, and Zimri; and Zimri begat Moza,
 And Moza begat Binea: Rapha was his son, Eleasah his son, Azel his son:
 And Azel had six sons, whose names are these, Azrikam, Bocheru, and Ishmael, and Sheariah, and Obadiah, and Hanan. All these were the sons of Azel.
American King James Version×—but here the purpose is to segue into the story of the tragic end of his life and reign related in the next chapter of Chronicles.