Sahih Muslim Book 6, Hadith Number 2506.

Chapter : Fasting on the day of ‘Ashura (1Oth of Muharram).

Ibn ‘Umar (Allah be pleased with them) said that the day of ‘Ashura was mentioned before the Messenger of Allah (may peace he upon him). Thereupon the Messenger of Allah,(may peace be upon him) said: That was a day on which the people of pre-Islamic days used to observe fast. So he who amongst you likes to observe fast should do so, and he who does not like it should abandon it.