The Northern layer originated among the Northern tribes that comprised the Kingdom of Israel, and other local traditions. From as early as the 9th century BC, these are among the earliest materials in the Hebrew Bible. They were adapted, expanded, or overwritten by later sources, following the Fall of its capital of Samaria to the Assyrians around 722 BC.
Traditionally called the Elohist (E) source, for its preference for Elohiym as the proper name of God, which it shares with the much later Priestly (P) source. Subsequent redactors sometimes overwrote Elohiym with Yahweh, to match their context.
The Hezekian layer originated in the southern kingdom of Judah, beginning with the reign of King Hezekiah, and his prophet, Isaiah. Especially following the fall of the North in 722 BC, the kingdom and the city of Jerusalem exploded in growth due to the influx of refugees from the North. Consequently, the themes of loyalty to the Lord's anointed king, the centrality of worship in the Jerusalem temple, and unity of the twelve tribes, became paramount to the survival of the "Sons of Israel."
It was historically called the Jawist (J) source (in German), for its preference for Yahweh as the proper name for God, in contrast to the earlier Northern (E) texts which preferred Elohiym. Once thought to be the oldest layer, it is more likely that it adapted and expanded earlier traditions.
The Josianic (D1) layer began with the reforms of King Josiah of Judah, Hezekiah's great-grandson, and his prophet, Jeremiah, with the discovery of the "Book of the Law" in the Temple in Jerusalem (2 Kings 22-23) around 622 BC. The massive reforms that followed emphasized a renewed commitment to the covenant, the study and keeping of the Torah, and warnings against the sin of idolatry.
It is often called the Deuteronomist (D1) source for its centrality to the book of Deuteronomy, whose core includes earlier sources, and its relationship with much of the books of Joshua through Kings, known as the Deuteronomistic History (DH), which were written in reflection of it.
The Exilic (D2) source is a continuation of the Josianic (D1) source, and often considered the same. The difference being whereas (D1) remains optimistic that Judah will heed the call to reform and obey the covenant, the Exilic (D2) knows that they will fail, and the result will be expulsion from the Promised Land and the Babylonian Exile following the destruction of Jerusalem in 586 BC (2 Ki 24:3-4; 25:21). Themes of remorse, guilt, and punishment are prominent in this source, as they are in second Jeremiah, Ezekiel, and Lamentations.
It is sometimes combined with the Josianic (D1) layer and simply called the Deuteronomist (D).
The Persian (P1) layer begins with the conquering of the Babylonians by the Persians in 539 BC, and the subsequent return Jewish exiles to Canaan. With a renewed sense of optimism, reflected in second Isaiah (40-55), the returning exiles saw the Exodus from Egypt and the conquest of Canaan as models for their return and reforming of their nation. Themes of forgiveness, generational promise, and renewal of covenant prevail.
The source is often combined with (P2) and simply called the Priestly (P), the difference being whereas the Persian (P1) has to do with the transition back to the Promised Land, the Priestly (P2) is much later after they are well established.
The Priestly (P2) is the final layer of the Hebrew Bible, beginning around the time of the building of the Second Temple around 516 BC. It redacted all the earlier layers and is responsible for the final version we have today. Produced by the priests who led Israel after the exile, it is focused on genealogies, lists, dates, festivals, separation from other nations, and especially holiness. Their job was to exile proof Israel, as is evident in Ezra, Nehemiah, and Malachi.
Once thought to be from the Kingdom period, the Priestly (P2) layer is often combined with the Persian (P1) layer, as both are post-exile. The Priestly (P2) layer is also believed to be responsible for the superscriptions in the Psalms.