"Behold! the angels said: "O Mary! Allah hath chosen thee and purified thee; chosen thee above the women of all nations. "O Mary! worship thy Lord devoutly; prostrate thyself and bow down (in prayer) with those who bow down."
Quran: Surah 3, Verse 42

The Qur'an further states that it is an awesome statement to accuse Mary of unchastity, as did the Jews:

"That they rejected faith: that they uttered against Mary a grave false charge."
Quran: Surah 4, Verse 156

In the Qur'an, Mary has been mentioned several time, especially in the chapters called “Al-Imran” and “Mariam”, the Arabic name for “Mary”.

When Mary was born, her mother prayed that her daughter should be given the protection of God so she would lead a good life. God heard her plea and accepted Mary into His protection, under the care of Zachariah, the father of John “the Baptist”.

Whenever Zachariah visited Mary in her sanctuary, he found her provided with food and upon questioning her, she would reply:

...He said: "O Mary! whence (comes) this to you?" She said: "From Allah: for Allah provides sustenance to whom He pleases without measure."
Quran: Surah 3, Verse 37

The Qur'an also gives an account of the birth of Jesus by Mary.

Just prior to Jesus’ birth, Mary retired to an eastern place where she prayed. It was in this state that the angel appeared to her in the shape of a man. As she thought the angel was a man, she was frightened and asked him not to invade her privacy:

She said: "I seek refuge from thee to (Allah) Most Gracious: (come not near) if thou dost fear Allah."
Quran: Surah 19, Verse 18

The angel then allayed Mary’s fears by saying:

He said: "Nay I am only a messenger from thy Lord (to announce) to thee the gift of a holy son."
Quran: Surah 19, Verse 19

Mary was naturally confused by this as she proclaimed that she had not been touched by any man to which the angel then replied:

He said: "So (it will be): thy Lord saith `That is easy for Me: and (We wish) to appoint him as a Sign unto men and a Mercy from Us': it is a matter (so) decreed."
Quran: Surah 19, Verse 21

The Qur'an continues the narration:

"So she conceived him and she retired with him to a remote place."
Quran: Surah 19, Verse 22

Mary, being human, suffered the effects of childbirth as any expectant mother would during these times then and in her anguish, she called:

"And the pains of childbirth drove her to the trunk of a palm-tree: she cried (in her anguish): "Ah! would that I had died before this! Would that I had been a thing forgotten and out of sight!" But (a voice) cried to her from beneath the (palm-free): "Grieve not! for thy Lord hath provided a rivulet beneath thee; "And shake towards thyself the trunk of the palm-tree: it will let fall fresh ripe dates upon thee. "So eat and drink and cool (thine) eye. And if thou dost see any man say `I have vowed a fast to (Allah) Most Gracious and this day will I enter into no talk with any human being.' "
Quran: Surah 19, Verses 23-26

When Mary showed the baby to her people, they said that this was truly an amazing thing that had happened. The newly born baby (Jesus) replied to the people:

He said: "I am indeed a servant of Allah: He hath given me revelation and made me a prophet; "And He hath made me Blessed wheresoever I be and hath enjoined on me Prayer and Charity as long as I live; "(He) hath made me kind to my mother and not overbearing or miserable; "So Peace is on me the day I was born the day that I die and the Day that I shall be raised up to life (again)"!
Quran: Surah19, Verses 30-33

Even though Mary is the mother of Jesus and occupies a highest position among the women, neither Mary nor Jesus have any divine attributes in them. The Holy Qur’an makes this clear in the following verse:

They do blaspheme who say: "Allah is Christ the son of Mary." But said Christ: "O children of Israel! worship Allah my Lord and your Lord." Whoever joins other gods with Allah, Allah will forbid him the garden and the Fire will be his abode. There will for the wrong-doers be no one to help.

They do blaspheme who say: Allah is one of three in a Trinity: for there is no god except One Allah. If they desist not from their word (of blasphemy) verily a grievous penalty will befall the blasphemers among them.

Why turn they not to Allah and seek His forgiveness? For Allah is Oft-forgiving Most Merciful. Christ the son of Mary was no more than an Apostle; many were the Apostles that passed away before him. His mother was a woman of truth. They had both to eat their (daily) food. See how Allah doth makes His Signs clear to them; yet see in what ways they are deluded away from the truth!

"Say: Will ye worship besides Allah something which hath no power either to harm or benefit you? But Allah He it is that heareth and knoweth all things." Say: "O people of the Book! exceed not in your religion the bounds (of what is proper) trespassing beyond the truth nor follow the vain desires of people who went wrong in times gone by who misled many and strayed (themselves) from the even way." Quran: Surah 5, Verses 72-77

"Say: He is Allah the One and Only; Allah the Eternal Absolute; He begetteth not nor is He begotten; And there is none like unto Him."
Quran: Surah 112

All Quranic quotations have been taken from the Abdullah Yusif Ali translation of “The Meaning of the Holy Qur’an”, published by Amana Corporation, Brentwood, Maryland, USA, 1993