The History of Gregorian Chant

The Gregorian Chant is the official chant of the catholic church since the Roman Rite.
It's a monocordic chant sung in unison without any instrument (musical accompaniment). Despite that today the catholic liturgy has more kind of sacred chant, it still saying that the Gregorian chant is the best way to connect the Man with God, the best way to express the prayers by the music.

an example of the one of the oldest notations of the Gregorian Chant

So, let's have a brief look about the History of this chant.
First the name: it's called Gregorian thanks to the Pope Gregory (590 - 604) who colected, selected, ordered the melodies heard in teh churches these dyas, making also some of them. Around the 12th century, it started to be called as plainchant, that comes from the latin "cantus plenus".
the first songs in Gregorian derivate from the songs sang in the jewish liturgy, including influences from the polytheist religions from the Roman Empire.
Using the existing melodies, the catholic church adopted tehm using the texts specially from the Bible, but also form the tradition. Until the 9th cnetury all the songs were transmited only oraly, which means a very hard work to memorize the songs.
So, to help the singers (the monks), in the end of the 9th century, the first music sheets appeared. The different kinds of notation appeared in orser to help to sing and to improve their capacity to sing new pieces without memorize them.
In the 10th century come the sript and the Dry lines drawn. In the beginning of the 10th century it's possible to determine the position for the semitones by the introduction of two lines: one red for the "Fa" and the other yellow for the "Do", and the use of letters for the clef: "C" and "F". But the changes didn't stop there.
In the second-half of the 11th century appeared the tetragramma, and the most perfect diastemasia is achieved. With all this evolution, it becomes possible to read a piece without a master.

An example of the quadratic notation.

But, meanwhile emerges the polyphonic melodie and the Gregorian chant started to die in the end of the 13th century. The Gregorian chant emerged again in 1845 when Danjou, an organist in Paris, has found the bilingual manuscrit of Montpellier. Since then, there wew many initiatives to study the ancient pieces of Gregorian chant and to introduce them again in the liturgy, thanks to the help of many personalities like: Fr Lambillote, Don Guéranger, Don Pothier, Don A. Mocquereau, Don J. Gajard, Cardinal Pizzardo, the Popes Pius X, Pius XI and Pius XII and the monks from Solesmes that published many works about this theme.
Despite the high number of notations, the most used now is the quadratic. And, since in the time where the Gregorian was born and diffused the communications were so difficult, we can find now in Europe many kinds of ways to write the Gregorian Chant.
The most important, just because it's the most studied now, is the notation from St. Gall, that emerged in the St. Gall monastery, in a region now in Switzerland.

St. Gall Monastery