The Mission of the Prophet (saw)

The Qur’an, the Book of Guidance revealed to the Prophet Muhammad (saw), describes his mission in the following verses:
"But it is nothing less than a Reminder to all Al Ameen (mankind, jinns and all that exists)" [Qur'an, al-Qalam 68:52]
"We have not sent you (O Muhammad) but as a mercy for Al Ameen (mankind, jinns and all that exists)" [Qur'an, al-Anbiyya 21:107]
"He it is Who has sent His Messenger with the Guidance and the Deen of Truth, to make it victorious over all (other) Deens even though the Mushrikeen (polytheists, pagans, idolaters, and disbelievers in the Oneness of Allah and in His Messenger) hate it" [Qur'an, as-Shaff 61:9]
"He it is Who has sent His Messenger with the Guidance and the Deen of Truth, that He may make it (Islam) superior over all religions. And Allah suffices as a Witness" [Qur'an, al-Fath 48:28]
"He it is Who has sent His Messenger with the Guidance and the Deen of Truth, to make it victorious over all (other) Deens even though the Mushrikeen (polytheists, pagans, idolaters, and disbelievers in the Oneness of Allah and in His Messenger) hate it" [Qur'an, at-Taubah 9:33]

Allah (swt) appointed Muhammad (saw) as His last Messenger with Guidance of Deen-Al-Haqq in order to make it dominate over all the other Batil (Falsehood). The way the Prophet Muhammad (saw) did his job is the only model available to us in its perfect form and in smallest detail.
"O Prophet (Muhammad)! Verily, We have sent you as witness, and a bearer of glad tidings, and a warner. And as the one who invites to Allah by His Leave, and as a lamp spreading light (through your instructions from the Qur’an and Sunnah" [Qur'an, al-Ahzab 33:45-46]
"And fight them until there is no more Fitnah (disbelief and worshipping of others along with Allah) and (all and every kind of ) worship is for Allah (Alone)..." [Qur'an, al-Baqarah 2:193]
Narrated Ibn ‘Umar (ra) :Allah’s Messenger (saw) said, "I have been ordered (by Allah) to fight against the people till they testify that La ilaha ill Allah wa Anna Muhammad Ar-Rasul Allah, and offer prayers perfectly (Iqamus-Salat) and give Zakat, so if they perform all that, then they save their lives, and properties from me except for Islamic laws, and their reckoning will be with Allah." (Bukhari)
"Indeed We have sent Our Messengers with clear proofs, and revealed to them the Scripture and the Balance (justice) that mankind be just. And We have brought forth iron wherein is mighty power (in matters of war), as well as many benefits for mankind, that Allah may test who it is that will help Him (His Deen), and His Messenger in the Unseen. Verily, Allah is All-Strong and All-Mighty" [Qur'an, al-Hadid 57:25]
The Prophet (saw) said: "Allah showed me all corners of the earth I saw its East and its West, and I saw that my Ummah will possess of it what He showed me from it." (Muslim, Abu Dawud, Ibn Majah, and Al-Timirdhi)
"This matter is as the day and night; Allah will make this Deen enter into every house of every inhabitant of the deserts, of villages, of towns, of cities, with either glory or disgrace. Allah will give glory to Islam, and Allah will bring disgrace upon disbelief (kufr)." (Ahmad ibn Hanbal, Al-Tabarani)

This address is for the Muslims to establish the Deen of Islam for the people of the world to live under, however, as individuals, they can remain in their religion as it is prohibited to force anybody to embrace Islam.

The Prophet’s (saw) call to mankind at large was to invite them to accept Allah’s authority without any partner in His Sovereignty. The entire struggle of his life was to eradicate the Batil/Shirk forces and establish Allah’s Deen in its place in totality.