Jewish calendar is a combination of lunar and solar way of time counting. After a long period of time counting based on witnesses (seeing young Moon, end of rainy season, ripe barley etc.) there was necessity for more precise way of counting when exactly holidays are coming. In the mid 4^th century Hilel 2^nd made pretty accurate calendar that was accepted by Sanhedrin of that time. From that time Jewish calendar has twelve months with 353, 354 or 355 days in non-leap years and 383, 384 and 385 days in leap years. Months have 30 or 29 days. Every third, eight, eleventh, fourteenth, seventeenth and nineteenth year one additional full 30-day month is added.

Before the Babylon slavery period there were no permanent names for months, or they are not known, except for a few names in Tanah. They were also named by ordinal numbers. During the Babylon slavery period Babylon names for months were adopted.

In leap years the first Adar has 30 days and Veadar has 29. The monhts are counted starting from Nissan respectively as shown above and the year is counting from Tishri. Days are still called after ordinal numbers:

Tradition of word of mouth says that Jewish counting of years starts from 3760 B.C. i.e. from the beginning of world. For example year 2005, till Rosh Hashanah, the first Tishri, in our calendar is the year of 5765.E.

Werber: Introduction to Jewish Religion