Is the celebration of the birthday (Mawlid) of our Prophet (Saw) halal?
All Praise to Allah Subhan o Taala and blessings on Prophet Muhammad peace be upon him His family and companions
References from Quran
In Surah Younis (10:58) Allah Swt says
قُلْ بِفَضْلِ اللَّـهِ وَبِرَحْمَتِهِ فَبِذَٰلِكَ فَلْيَفْرَحُوا هُوَ خَيْرٌ مِّمَّا يَجْمَعُونَ
Say: "In the bounty of Allah. And in His Mercy,- in that let them rejoice": that is better than the (wealth) they hoard.
Hazrat Ibn Abbas Ra who got the title of Tarjuman ul Quran as his Tafsir expertise He stated that in this ayah the bounty refers to Ilm (Knowledge) and Mercy refers to Prophet Muhammad ﷺ.
"And We have not sent you, [O Muhammad], except as a Mercy to the worlds".Quran 21:107
This clearly shows that it is not only allowed to do celebration rather it is very Mustahab and preferable as Allah Swt says in that ayah to rejoice or celebrate the bounties and Mercy given by Allah Swt and Our Prophet indeed is the biggest mercy and blessing to the whole universe.
الْيَوْمَ أَكْمَلْتُ لَكُمْ دِينَكُمْ وَأَتْمَمْتُ عَلَيْكُمْ نِعْمَتِي وَرَضِيتُ لَكُمُ الْإِسْلَامَ دِينًا
This day I have perfected for you your religion and completed My favor(Na'mat) upon you and have approved for you Islam as religion.Quran (5:3)
وَأَمَّا بِنِعْمَةِ رَبِّكَ فَحَدِّثْ And abundantly proclaim the favours(Na'mat) of your Lord.Quran 93:11
Now in Surah Al-Imran verse 81 Allah Swt talks about an event where all prophets were present and Allah Swt mentions arrival or birth of a Prophet Muhammad ﷺ
And remember when Allah took a covenant from the Prophets; “If I give you the Book and knowledge and the (promised) Noble Messenger (Prophet Mohammed – peace and blessings be upon him) comes to you, confirming the Books you possess, you shall positively, definitely believe in him and you shall positively, definitely help him”; He said, “Do you agree, and accept My binding responsibility in this matter?” They all answered, “We agree”; He said, “Then bear witness amongst yourselves, and I Myself am a witness with you.”(Quran)
So it is Sunnah of Allah Swt to hold these gatherings where we do remebrance of His Messenger.
References from Ahadith
We could see the importance of Birthday of prophet Muhammdﷺ from this hadith
Abu Qatada Ansari (Allah be pleased with him) reported that Allah's Massenger (ﷺ) was asked about fasting on Monday, whereupon he said: It is (the day) when I was born and revelation was sent down to me.(Muslim)
The day when I was born is same as "birthday".
Abu lahab torment was relieved because he freed slave girl thuwaiba when she announces birth of Prophet Muhammadﷺ.
".....Narrated 'Urwa: Thuwaiba was the freed slave girl of Abu Lahb whom he had manumitted, and then she suckled the Prophet. When Abu Lahb died, one of his relatives saw him in a dream in a very bad state and asked him, "What have you encountered?" Abu Lahb said, "I have not found any rest since I left you, except that I have been given water to drink in this (the space between his thumb and other fingers) and that is because of my manumitting"(Bukhari)
It was narrated that Abu Sa'eed Al-Khudri said: "Mu'awiyah, (may Allah be pleased with him,) said: 'The Messenger of Allah [SAW] went out to a circle - meaning, of his Companions - and said: 'What are you doing?' They said: 'We have come together to pray to Allah and praise Him for guiding us to His religion, and blessing us with you.' He said: 'I ask you, by Allah, is that the only reason?' They said: 'By Allah, we have not come together for any other reason.' He said: 'I am not asking you to swear to an oath because of any suspicion; rather Jibril came to me and told me that Allah, the Mighty and Sublime, is boasting of you to the angels.'"(Nasai)
This showed that Sahaba noble companions of Prophet Muhammad ﷺ celebrated and held a gathering same as people gather now and do zikrullah, praising Messenger,telling miracles of Prophet Muhammad ﷺ, sending salat o salam and all these are very preferred acts proven from Sunnah of Allah Swt, Sunnah of His Habib Muhammad ﷺ and Sunnah of Sahaba his Noble companions.
There are 50 muslim Majority countries in the world out of which 47 countries (except for Saudi arab and Qatar) Alhudulillah celebrate birth of prophet Muhammad peace be upon him and 47 countries announces official Holiday on this special day.(These countries from Asia are Afghanistan,Bangladesh,Brunei,India,Indonesia,Pakistan,Malaysia,Sirilanka,Uzbekistan,,,,From Middle East are Bahrain,Iraq,Iran,Jordan,Kuwait,lebanon,Iraq,Palestine,Syria,UAE,Yemen,Except for SaudiaArab,Qatar,Israil all eleven out of 14 Arab countries officially celebrate Mawlid or Milad.From Africa Egypt,Algeria,Mali,Libiya,Morocco,Mauritania,Niger,Nigeria,Senegal,binin,Barkinafaso,Comoros,Cameron,Djibouti,Eritria,CoteDilwoire,Ethiopia,gambia,Ghana,Guinea,Sierraleone,Somalia,Sudan,tanzania, Togo,Tunisia,,,,Other Than these Fiji and Guyana also officially celebrate Birth of our beloved Prophet Muhammad peace be upon him.So more than 85% of world Islamic population Celebrate and recieve blessings of Allah Swt.
Also see the Fatwa from Daralifta Misr http://www.dar-alifta.org/ViewFatwa.aspx?ID=140&LangID=2
Allah Swt and His Messenger knows best.