The Jewish calendar that dates from the time of Hillel II (359 C.E., A.M. 4119) is the official calendar of the State of Israel. It is a lunisolar calendar based on computations rather than visual observations (visual observations of the young crescent Moon were used in ancient times). The count of years begins with 1 Tishri A.M. 1 (Anno Mundi), which corresponds to Monday, 7 October 3761 B.C.E. (proleptic Julian calendar). Passover begins on the same liturgical date, Nisan 15, each year. The dates for the first day of Passover for the years 360 C.E. or later using the civil calendar (Julian or Gregorian) are available here.
For further information on calendars, see Richards, E.G. 2012, "Calendars," from the Explanatory Supplement to the Astronomical Almanac, 3rd edition, S.E Urban and P.K. Seidelmann eds., (Mill Valley, CA: University Science Books), Chapter 15, pp. 585-624.
Most books on calendars describe the details of the Jewish calendar.