It is a direct quote from the Gospel of Luke (Luke 1:46-55), and is the speech given by Mary at the her Visitation to her cousin Elizabeth.
Because it is directly from scripture, there are number of different translations: as well as the biblical translations, many churches have their own authorised translation for use in daily prayer.
There are also many musical settings of the prayer, ranging from complex multi-part harmonies, to simple folk tunes.
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Full text - ICEL Translation
My soul proclaims the greatness of the Lord,
my spirit rejoices in God my Saviour
for he has looked with favour on his lowly servant.
From this day all generations will call me blessed:
the Almighty has done great things for me, and holy is his Name.
He has mercy on those who fear him in every generation.
He has shown the strength of his arm,
he has scattered the proud in their conceit.
He has cast down the mighty from their thrones,
and has lifted up the lowly.
He has filled the hungry with good things,
and the rich he has sent away empty.
He has come to the help of his servant Israel
for he has remembered his promise of mercy,
the promise he made to our fathers,
to Abraham and his children for ever.
Full text - BCP Translation
My soul doth magnify the Lord and my spirit hath rejoiced in God my Saviour.
For he hath regarded the lowliness of his handmaiden.
For behold, from henceforth all generations shall call me blessed.
For he that is mighty hath magnified me and holy is his Name.
And his mercy is on them that fear him throughout all generations.
He hath shewed strength with his arm he hath scattered the proud in the imagination of their hearts.
He hath put down the mighty from their seat and hath exalted the humble and meek.
He hath filled the hungry with good things and the rich he hath sent empty away.
He remembering his mercy hath holpen his servant Israel as he promised to our forefathers, Abraham and his seed for ever.
Glory Be to the Father, and to the Son, and to the Holy Ghost;
As it was in the beginning, is now, and ever shall be, world without end. Amen.