Question Summary:
Is it from Sunnah to keep a lot of nafil fasts in the month of Muharram?

Question Detail:

Is it from Sunnah to keep a lot of nafil fasts in the month of Muharram?

Answer :

In the Name of Allah, the Most Gracious, the Most Merciful.
As-salāmu ‘alaykum wa-rahmatullāhi wa-barakātuh.
Muharaam is the first month of the Islamic Hijri calendar and it is amongst the four sacred months namely Zulqada, Zulhijja, Muharram and Rajab. Allah Taala mentions in the Quraan:
إِنَّ عِدَّةَ الشُّهُورِ عِنْدَ اللَّهِ اثْنَا عَشَرَ شَهْرًا فِي كِتَابِ اللَّهِ يَوْمَ خَلَقَ السَّمَاوَاتِ وَالْأَرْضَ مِنْهَا أَرْبَعَةٌ حُرُمٌ ذَلِكَ الدِّينُ الْقَيِّمُ فَلَا تَظْلِمُوا فِيهِنَّ أَنْفُسَكُمْ وَقَاتِلُوا الْمُشْرِكِينَ كَافَّةً كَمَا يُقَاتِلُونَكُمْ كَافَّةً وَاعْلَمُوا أَنَّ اللَّهَ مَعَ الْمُتَّقِينَ
The number of months according to Allah is twelve months (mentioned) in the Book of Allah on the day in which He created the heavens and the earth. Among these (twelve months) there are four sanctified months. (Surah Tawba-36)
It is also mentioned in a hadith:
عَنْ أَبِي بَكْرَةَ رَضِيَ اللَّهُ عَنْهُ، عَنِ النَّبِيِّ صَلَّى اللهُ عَلَيْهِ وَسَلَّمَ قَالَ... السَّنَةُ اثْنَا عَشَرَ شَهْرًا، مِنْهَا أَرْبَعَةٌ حُرُمٌ، ثَلاَثَةٌ مُتَوَالِيَاتٌ: ذُو القَعْدَةِ وَذُو الحِجَّةِ وَالمُحَرَّمُ، وَرَجَبُ مُضَرَ، الَّذِي بَيْنَ جُمَادَى وَشَعْبَانَ 
Nabi Salallahu Alaihi Wasallam said a year has twelve months and from which four are sanctified months, three of them are in sequence namely Zulqada, Zulhijja, Muharram and Rajab which is between Jumadal Ukhra and Shaaban (Bukhari p454 Qadeemi)
 
 
It is mentioned in a hadith:
عَنْ أَبِي هُرَيْرَةَ رَضِيَ اللهُ عَنْهُ، يَرْفَعُهُ... وَأَفْضَلُ الصِّيَامِ بَعْدَ شَهْرِ رَمَضَانَ، صِيَامُ شَهْرِ اللهِ الْمُحَرَّمِ»
The best fast after the fast of Ramadan are those of the month of Muharram (Muslim p368 Qadeemi)
Although the fasts of Muharram are not obligatory, yet, it is clear from the above hadith that the non-obligatory fast of Muharram are most rewardable amongst optional fasts.[1]
Besides the whole month of Muharram being blessed and sacred, the tenth of Muharram specially holds great significance and it is known as ‘Ashurah’. It is mentioned in a hadith:
عَنِ ابْنِ عَبَّاسٍ قَالَ: لَمَّا قَدِمَ النَّبِيُّ صَلَّى اللهُ عَلَيْهِ وَسَلَّمَ الْمَدِينَةَ وَجَدَ الْيَهُودَ يَصُومُونَ عَاشُورَاءَ، فَسُئِلُوا عَنْ ذَلِكَ، فَقَالُوا: هَذَا الْيَوْمُ الَّذِي أَظْهَرَ اللَّهُ فِيهِ مُوسَى عَلَى فِرْعَوْنَ وَنَحْنُ نَصُومُهُ تَعْظِيمًا لَهُ، فَقَالَ رَسُولُ اللَّهِ صَلَّى اللهُ عَلَيْهِ وَسَلَّمَ: «نَحْنُ أَوْلَى بِمُوسَى مِنْكُمْ»، وَأَمَرَ بِصِيَامِه 
Ibn Abbas Radiallahu Anhu narrates that when the prophet of Allah Salallahu Alaihi Wasallam migrated to Madina the Jews of Madina would fast on the tenth of Muharram. They said it was the day when Allah Taala helped Musa Alaihi Salam cross the sea and drowned the Pharaoh. Rasulullah Salallahu Alaihi Wasallam said we are closer to Musa Alaihi Salam than you and he (Salallahu Alaihi Wasallam) ordered the people to fast on Ashurah. (Abu Dawood p331 Rashediyah)[2]
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And Allah Ta’āla Knows Best
Ismail Dawoodjee
Student Darul Iftaa
Zambia
Checked and Approved by,
Mufti Ebrahim Desai.
www.daruliftaa.net 
التطوع المطلق بالصوم فهاذا افضله المحرم كما ان افضل التطوع المطلق بالصلاة قيام اليل (لطائف المعارف ص78 ابن كثير)[1]
Islamic Months Merits and Precepts [2]