Imam Al-Nawawi's Riyad-us-Saliheen
Chapter 229
The Desirability of Observing Saum (Fasting) on Monday and Thursday

1255. Abu Qatadah (May Allah be pleased with him) reported: The Messenger of Allah (sallallaahu ’alayhi wa sallam) was asked about fasting on Mondays. He said, "That is the day on which I was born and the day on which I received Revelation.''
[Muslim].

Commentary:  This Hadith points out the excellence of fasting on Mondays. The reason behind this, as is stated in the Hadith, is that the Prophet (sallallaahu ’alayhi wa sallam) was born on it and that it was the day on which he received the first Revelation. It coincided with the 17th Ramadan as well.

1256. Abu Hurairah (May Allah be pleased with him) reported: The Messenger of Allah (sallallaahu ’alayhi wa sallam) said, "Deeds of people are presented (to Allah) on Mondays and Thursdays. So I like that my actions be presented while I am fasting.''
[At-Tirmidhi].

Commentary:  Observance of Saum on Monday and Thursday is Mustahabb (desirable), and the reason for its being so has been mentioned in the Hadith.

1257. `Aishah (May Allah be pleased with her)u reported: The Messenger of Allah (sallallaahu ’alayhi wa sallam) used to observe fast on Mondays and Thursdays.
[At-Tirmidhi].

Commentary:  "Yataharra" in the Hadith means to seek and search, that is, he (sallallaahu ’alayhi wa sallam) used to make special arrangements for it. The reason he was so particular about these Saum has been mentioned in the previous Hadith.