Determining what marks a new year is a bit complicated. Based on Exodus 12:2, Nisan is considered the first month of the year. However, the year number changes on Rosh Hashanah, which is on the first of Tishrei, the seventh month of the religious year. Then there is Tu B'Shvat (15 Shvat), which is the new year "for trees."
The best way to understand this is that the Jewish calendar simply has different "years" for different purposes, just as the secular world recognizes as fiscal year, a school year and a calendar year. The bottom line: Nisan is the first month on the Jewish calendar and Rosh Hashanah (on 1 Tishrei) is the "Jewish New Year."
The year number on a Jewish calendar is based on a traditional date of creation, based on adding up the geneaologies in the Tanakh. The Jewish year 5764 began on September 27, 2003. For convenience, many Jews use the Christian dating of years, but with the designation CE (Common or Christian Era) instead of AD (anno domini, "in the year of our Lord"). To use the latter expression, even in abbreviation, would be to falsely (and blasphemously) imply faith in Jesus as Lord.
The months of the Jewish calendar are as follows:
|Number of Days||Gregorian Equivalent||Holidays in This Month|
|Av||30||July-August||Tisha b'Av (9th)|
|Tishri||30||September-October||Rosh Hashanah (1st) |
Yom Kippur (10th)
|Kheshvan||29 or 30||October-November|
|Kislev||29 or 30||November-December||Hanukah (25th)|
|Shevat||30||January-February||Tu b'Shevat (15th)|
|Adar||29 (30 in a leap year)||February-March||Purim (14th)|
|Adar II||(29 in a leap year)||March-April||Purim (14th; leap year only)|