According to the majority opinion, Rasulullah (Sallallaahu Alayhi Wasallam) was born in the month of Rabi-ul-Awwal, in the year of the elephant. The day of his birth was Monday.
Hadhrat Abu Qataadah (Radhiallaahu Anhu) narrates that Rasulullah (Sallallaahu Alayhi Wasallam) was asked regarding the fast of Monday. He replied, ?It is the day I was born and also the day when the first revelation was sent upon me.? (Muslim vol1 pg.368; Deoband).
There are differences of opinion on the date of Rasulullah’s (Sallallaahu Alayhi Wasallam) birth. Allaamah Kawthari (RA) prefers the 9th of Rabi-ul-Awwal. (Maqaalaatul Kawthari pg.405 – 207). Allaamah Qastalaani (RA) states that the majority of the Muhadditheen and historians have also preferred the 9th of Rabi-ul-Awwal.
Rasulullah (Sallallaahu Alayhi Wasallam) passed away in Rabiul-Awwal on a Monday. As regards the date of his demise, there are three opinions: 1, 2 and 12 Rabi-ul-Awwal (Bidaaya Wan Nihaaya vol.5 pg.275)
The 9th Dhul-Hijjah (day of Arafah) in the year 10AH (the year which Rasulullah (Sallallaahu Alayhi Wasallam) performed Hajj) was a Friday. If the months Dhul-Hijjah, Muharram and Safar, all were 30 days, or 29 days or some 29 and others 30 days, the 12th Rabi-ul-Awwal did not fall on a Monday. Therefore, the preferred view of the date of Rasulullah’s demise is the 1st or 2nd Rabi-ul-Awwal. Ibn Jarir (RA) prefers the 1st Rabi-ul-Awwal while Ibn Hajar prefers the 2nd Rabi-ul-Awwal. (Al-Mawaahib with Zarqaani vol.1 pg.131)