Which Hebrew month immediately follows Kislev?

The Hebrew month that immediately follows Kislev is Tevet.

Kislev is the ninth month of the Hebrew calendar when the months are counted in the traditional ecclesiastical sequence. Tevet follows it as the tenth month and precedes Shevat. Because the Hebrew calendar is lunisolar, these months shift against the Gregorian calendar, usually falling across December and January.

Hanukkah begins on 25 Kislev and commonly continues into Tevet. In a typical year it ends on 2 Tevet, though it can end on 3 Tevet when Kislev has only 29 days. Tevet itself always has 29 days in the fixed Hebrew calendar.

Readers sometimes confuse the month order because Hebrew months have both religious and civil numbering systems. Tevet is the tenth month in the religious or biblical count, but the fourth month in the civil-year count beginning with Tishrei. Shevat comes next, while Cheshvan precedes Kislev and Adar occurs later in the year.