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The first day of Shawwal, marking the end of Ramadan's fast.
Eid al-Fitr falls on the 1st of Shawwal, immediately after Ramadan, and is a day of joy and gratitude for having been enabled to fast and worship through the month. The Qur'an ties the end of the fast directly to remembrance and thanks: '...that you complete the number [of days] and that you glorify Allah for that He has guided you, and that you may be grateful' (Qur'an 2:185).
Fasting on this day is expressly forbidden, not merely discouraged — the Prophet ﷺ named it, alongside Eid al-Adha, as one of the two days on which Muslims are commanded to eat rather than fast (Bukhari 1990). The day begins with Zakat al-Fitr and the Eid prayer, and continues with visiting family, exchanging good wishes, and general festivity within Islamic bounds.

Qur'an

Reference: Qur'an 2:185
...that you complete the number [of days] and that you glorify Allah for that He has guided you, and that you may be grateful.

Hadith

Sahih al-Bukhari · 1990
Sahih
These are two days on which the Messenger of Allah ﷺ forbade fasting: the day you break your fast (of Ramadan), and the day on which you eat from your sacrifice.
Educational overview — not a fatwa. Where schools differ (such as the extra-takbir count), both positions are presented; follow your imam or a qualified local scholar.