كتاب الصيام
13  
The Book of Fasting
(19)
Chapter: Fasting on the day of Ashura'
(19)
باب صَوْمِ يَوْمِ عَاشُورَاءَ ‏‏
Sahih Muslim 1129 a

Abd al-Rahman reported that he heard Mu'awiya b. Abu Sufyan delivering a sermon in Medina. i. e. when he came there (for Hajj). He delivered a sermon on the day of 'Ashura and said:

People of Medina, where are your scholars? I heard the Messenger of Allah (ﷺ) say on this very day: It is the day of 'Ashura. Allah has not made fasting on This day obligatory for you but I am fasting. He who likes to observe fast among you should do so, and he who likes not to observe it may not observe it.
حَدَّثَنِي حَرْمَلَةُ بْنُ يَحْيَى، أَخْبَرَنَا ابْنُ وَهْبٍ، أَخْبَرَنِي يُونُسُ، عَنِ ابْنِ شِهَابٍ، أَخْبَرَنِي حُمَيْدُ بْنُ عَبْدِ الرَّحْمَنِ، أَنَّهُ سَمِعَ مُعَاوِيَةَ بْنَ أَبِي سُفْيَانَ، خَطِيبًا بِالْمَدِينَةِ - يَعْنِي فِي قَدْمَةٍ قَدِمَهَا - خَطَبَهُمْ يَوْمَ عَاشُورَاءَ فَقَالَ أَيْنَ عُلَمَاؤُكُمْ يَا أَهْلَ الْمَدِينَةِ سَمِعْتُ رَسُولَ اللَّهِ صلى الله عليه وسلم يَقُولُ لِهَذَا الْيَوْمِ ‏ "‏ هَذَا يَوْمُ عَاشُورَاءَ وَلَمْ يَكْتُبِ اللَّهُ عَلَيْكُمْ صِيَامَهُ وَأَنَا صَائِمٌ فَمَنْ أَحَبَّ مِنْكُمْ أَنْ يَصُومَ فَلْيَصُمْ وَمَنْ أَحَبَّ أَنْ يُفْطِرَ فَلْيُفْطِرْ ‏"‏ ‏.‏
Reference : Sahih Muslim 1129a
In-book reference : Book 13, Hadith 159
USC-MSA web (English) reference : Book 6, Hadith 2515
  (deprecated numbering scheme)