كتاب صلاة المسافرين وقصرها
6  
The Book of Prayer - Travellers
(25)
Chapter: Encouragement to pray qiyam during Ramadan, which is Tarawih
(25)
باب التَّرْغِيبِ فِي قِيَامِ رَمَضَانَ وَهُوَ التَّرَاوِيحُ ‏
Sahih Muslim 761 a

'A'isha reported that the Messenger of Allah (ﷺ) prayed one night in the mosque and people also prayed along with him. He then prayed on the following night and there were many persons. Then on the third or fourth night (many people) gathered there, but the Messenger of Allah (ﷺ) did not come out to them (for leading the Tarawih prayer). When it was morning he said:

I saw what you were doing, but I desisted to come to you (and lead the prayer) for I feared that this prayer might become obligatory for you. (He the narrator) said: It was the month of Ramadan.
حَدَّثَنَا يَحْيَى بْنُ يَحْيَى، قَالَ قَرَأْتُ عَلَى مَالِكٍ عَنِ ابْنِ شِهَابٍ، عَنْ عُرْوَةَ، عَنْ عَائِشَةَ، أَنَّ رَسُولَ اللَّهِ صلى الله عليه وسلم صَلَّى فِي الْمَسْجِدِ ذَاتَ لَيْلَةٍ فَصَلَّى بِصَلاَتِهِ نَاسٌ ثُمَّ صَلَّى مِنَ الْقَابِلَةِ فَكَثُرَ النَّاسُ ثُمَّ اجْتَمَعُوا مِنَ اللَّيْلَةِ الثَّالِثَةِ أَوِ الرَّابِعَةِ فَلَمْ يَخْرُجْ إِلَيْهِمْ رَسُولُ اللَّهِ صلى الله عليه وسلم فَلَمَّا أَصْبَحَ قَالَ ‏ "‏ قَدْ رَأَيْتُ الَّذِي صَنَعْتُمْ فَلَمْ يَمْنَعْنِي مِنَ الْخُرُوجِ إِلَيْكُمْ إِلاَّ أَنِّي خَشِيتُ أَنْ تُفْرَضَ عَلَيْكُمْ ‏"‏ ‏.‏ قَالَ وَذَلِكَ فِي رَمَضَانَ ‏.‏
Reference : Sahih Muslim 761a
In-book reference : Book 6, Hadith 211
USC-MSA web (English) reference : Book 4, Hadith 1666
  (deprecated numbering scheme)