The Hebrew calendar is used in Judaism for the observance of religious holidays.
It is also the official calendar in Israel. But the Gregorian calendar is used for any secular purpose.
It is based both on the movements of the moon
and the seasons of the Earth, so as to observe the festivals of the Torah.
In the ancient times, the sages of the Sanhedrin (abbinical court, by the Temple of Jerusalem) received the testimony of eyewitnesses who saw the new moon.
When the Sanhedrin, after verification, decreed on Rosh Chodesh (new month), information
was spread to neighboring cities, and step by step to the full extent of the Jewish people.
At the turn of the month of Nissan, if signs of spring were not visible out in the fields, an intercalary month was inserted,
to observe the feast of Pesach in the spring.
Later, after the conquest of Jerusalem by the Roman Empire, and while the very existence of the Sanhedrin was threatened, Rabbi Hillel
son of Yehuda ha-Nasi, who headed the Sanhedrin, established in the year 358 of the current era the calculation rules of the calendar
in order to make possible its observance throughout the world.
This site presents the peculiarities of the Jewish calendar, the astronomical and natural phenomena that make its rhythm, et the religious events of which it is a base.
I also propose a calculation method for establishing a perpetual calendar, and some tools for manipulating Jewish and secular dates, from one system to the other.