In my books on prophecy and chronology, I have used selected chronologies from the Seder Olam, the basic text on which all historical understanding of Jewish tradition in the Talmud is based. I do so mainly as a way of cross-checking the biblical chronology.
For example, the Seder Olam says that there were 155 years from the year that Solomon finished building and dedicating the Temple until the year that Joash renovated the Temple in his 23rd regnal year, and that there were 218 years from the renovation by Joash until the renovation by Josiah in his 18th regnal year, which is known to have begun in 622 BCE. Using this information, one can compute that the 23rd regnal year of Joash was the year 840 BCE (622 BCE + 218 years), and that Solomon completed and dedicated the Temple in 995 BCE (840 BCE + 155 years). This cross-references perfectly with what I calculated from the chronology for the kings of Israel and Judah (and the construction of the Temple) given in biblical text, using the chronology provided in Daniel, chapter 4, to calculate the start of the divided monarchal period. Thus, the Seder Olam can be used as a cross-check on occasion, although it can never be used as the primary source in biblical interpretation. That role is reserved for the biblical text itself.
Seder Olam, the name generally used in biblical chronological circles to denote a work also known as the Seder Olam Rabbah (סדר עולם רבה, “The Long Order of the World”), is a book of Jewish rabbinical chronology explaining biblical events from the Creation down to the end of the Achaemenid Persian Period and the advent of Alexander the Great on the world stage in 331 BCE, with a brief mention of the later bar Kochba revolt in 132-135 CE. It was compiled from traditional Hebrew records edited into a single volume by the famous early Talmudist, Rabbi Yose ben Halafta, around 160 CE. It has 30 chapters, formed into three thematic “gates,” each encompassing ten chapters. The purpose of the work appears to be calendrical, with specific dates given for various biblical events, and with comments that seek to explain the many chronological difficulties found throughout the Hebrew biblical text.
In working out the chronology of the kings of Israel and Judah for my book Sacred Chronology of the Hebrew Kings, I have found that the Seder Olam is fairly accurate with regards to its chronological relationships, such as the example about the Temple given in the paragraph above, but not necessarily in its exact dates. For the dates after the Exile, the chronology in the Seder Olam seems to have been subject to error, either accidental due to the turmoil of the times, or perhaps even intentional later on to counter Christian exegesis of Daniel 9:24-27 relating to Jesus. For instance, the Persian Period is shortened to only 34 years in duration (52 years in French manuscripts), probably to accommodate an erroneous rabbinical interpretation derived from Daniel, chapter 9, that interprets that passage to say that the time between the destruction of the First Temple and the Second Temple had to be 490 years. Historians almost universally agree that the First Temple was destroyed by the Babylonians in 586 BCE, but the Seder Olam gives the destruction as occurring in the year 423 BCE, a 165-year difference (allowing for overlap on both ends), in this way allowing it to conform to the incorrect 490-year rabbinic interpretation about the two Temple destructions. The duration of the Persian Period is arbitrarily shortened in the Seder Olam to accommodate the rabbinical Temple chronology.
Wikipedia says this: “The dates of events in Jewish history are often expressed in relation to the Gregorian calendar. For example, the Jewish date for the destruction of the First Temple (3338 AM = 423 BCE) differs from the modern scientific date, which is usually expressed using the Gregorian calendar as 586 BCE. Implicit in this practice is the view that if all the differences in structure between the Hebrew and Gregorian calendars are taken into consideration, the two dates can be derived from each other. This is not the case. If the traditional dates of events before the Second Temple era are assumed to be using the standard Hebrew calendar, they refer to different objective years than those of the secular dates. The discrepancy is some 165 years.”
My use of the Seder Olam is confined to cross-checking the biblical chronology derived from the Masoretic text that is the basis of the modern English translations of the Tanakh, especially for the chronology associated with the period of the divided monarchies of Israel and Judah. I emphasize again, however, it is never used as the primary source to supplant the biblical text. However, the Seder Olam can be a useful work for cross-checking and verifying with a second witness the chronological details of events and time periods that occurred before the Exile, but only after the overall chronology has been derived from the biblical text.