All praise is due to Allah, may peace and blessings be upon our Prophet Muhammad, his family and all his Companions.

Fasting six days of Shawwaal is a sunnah that brings great reward according to the following narration.

Abu Ayyoob al-Ansaaree (may Allaah be pleased with him) reported that the Messenger of Allaah (peace and blessings of Allaah be upon him)  said; 'Whoever fasts the month of Ramadhaan and follows it by six of Shawwaal then as if he has fasted for ever.' Narrated Muslim

The hadith is also narrated by Al-Tirmidhi, Abu-Dawood, Ibn-Maajah, Ahmad and Ad-Daarimi.

Imam Ahmad (may Allaah have mercy on him) also recorded from Jabir bin Abdullaah al-Ansaaree (may Allaah be pleased with him) that the Messenger of Allaah (peace and blessings of Allaah be upon him)  said; 'Whoever fasts the month of Ramadhaan and six of Shawwaal then as if he has fasted for the whole year.'

Imam Tirmidhi (may Allaah have mercy on him) said that Abu Ayyoob's report is Hassan Saheeh.

It was reported by Thawbaan, the freed slave of the Messenger of Allaah that he heard the Messenger of Allaah (peace and blessings of Allaah be upon him) saying: 'Allaah has made the reward of every good deed ten times so the month is like ten months and adding six days after Eid-ul-Fitr complete a year.' Sunan-al-Nasaaie al-Kubraa 2861

Imam Al-Nawwawi (may Allaah have mercy on him) said that it is preferred that one fasts six consecutive days after Eid-ul-Fitr, but even if this is done non consecutively one achieves the benefit of, following Ramadhaan with six of Shawwal.

Ibn-Qudaamah (may Allaah have mercy on him) said "there is no difference in fasting these consecutively or separate, whether in the beginning of month or towards the end" al-Mughnee.

In fact some scholars are of the view that it should not be done regularly and strictly straight after Eid as it may turn into an innovation.

It is important to know that fasting on the day of Eid is haraam.

It is also important to note if one is to earn the reward mentioned in the hadeeth he should make up for any missed fasts of Ramadhaan before fasting the six days of Shawwaal, as the Messenger of Allaah (peace and blessings of Allaah be upon him)  said; "whoever fasts the month of Ramadhaan and follow it by six of Shawwaal."

Another important point is that one can not fast by making the niyyah (intention) of an obligatory missed fast and a non-obligatory fast of Shawwaal at the same time.

And Allah the Most Knowledgeable knows what is best and most correct.

May Allaah Subhanahu-wa-Ta’alaa help and guide us to do all that He is pleased with and his Peace and blessings be upon His last Prophet Muhammad.