Fasting Six Days of Shawwal After Ramadan: "Like Fasting The Entire Year"
The Messenger of Allah (blessings and peace be upon him) said,
"Whoever fasts Ramadan and follows it with six days from Shawwal it is as if they fasted the entire year." [Hadith-Muslim]
NB. It is permitted to fast these six days separately throughout the month, or consecutively, after Eid al-Fitr. It is prohibitively disliked (makruh tahriman) and sinful to fast on Eid day itself.