(1) Gaayatree Chhand
A type of Chhand - meter of poetry. According to Padm Puraan, p 924, there is a Daivee Gaayatree Chhand. "Daivyekam" - according to this Pingal Sootra, 1-letter or a Chhand of 1-Pad of 8-letters is Daivee Gaayatree Mantra. According to 1-letter, Pranav Mantra (Aum) is considered as Daivee Gaayatree Mantra; and according to the second meaning any 8-letter Mantra may be called Daivee Gaayatree Mantra. Both Daivee Gaayatree Mantras are called "Ekaaksharaa" and "Ek-Padaa" Gaayatree respectively. The 24-letter famous Gaayatree is called "Tri-Padaa Gaayatree" because of consisting of 3-Pad (3 Charan or 3 lines) of 8 letters each.

(2) Gaayatree Mantra
Any Mantra may be called Gaayatree Mantra if it satisfies Gaayatree Chhand's requirements. But there is a special Mantra which is well known as Gaayatree Mantra, that is Verse 3-62-10 of Rig Ved, more popularly known as Gaayatree Mantra because of its meter --

Om Bhoor Bhuvah Swaha, Tat Savitur Varenyam. Bhargo Devasya Dheemahi Dhiyonah Prachodayaat||

This Mantra is popularly called Gaayatree Mantra because it is devoted to Saavitree (or Gaayatree) Devee.

This is Rig Ved Mantra - 3-62-10. The actual Mantra starts from "Tat Savi Tur....". But Aum is always added to Mantra; and "Bhoor Bhuvah Swaha" is called Vyaahrit, which means "Earth, sky, and Heaven", is also added to the Mantra. These words are often added to important Mantra. According to Padm Puraan, 3/4  "There are three Sanaatan Vyaahriti - Bhoo, Bhuvah and Swaha. These have been added to Gaayatree Mantra. They destroy all kinds of ill omens. These three have been regarded as the symbol of Pradhaan, Purush and Kaal; Vishnu, Brahmaa and Mahaadev; and Sat, Raj and Tam Gun respectively."

The meaning of this Mantra is - "The Earth, the sky and the Heaven praise Him. Let us meditate on the Supreme Glory of the Divine Lord. He is the One who sustains us. We pray to Him that He may direct our understanding by instilling wisdom in us."

This Mantra is the most sacred Mantra of the Hindu for the very good reason that it asks God to provide the worshipper with wisdom. There is no greater Mantra than Gaayatree Mantra for Jap. Its real name is Saavitree Mantra, because in this Mantra God is addressed as Savitra. Some ignorant people have declared Gaayatree the name of Goddess. The Drashtaa (not Srishtaa) of this Mantra is Maharshi Vishwaamitra Jee and it is devoted to Soorya Dev.

Where it is Found
This Mantra is found in 3 out of 4 Ved, 4 times, although in different versions.
Rig Ved     -    3-62-10 -     Begins with "Tat Savitur Varenyam..."
Yajur Ved  -   22-9 -          Begins with "Aum Bhoor Bhuvah Swaha..."
Yajur Ved  -   36-3 -          Begins with "Bhoor Bhuvah Swaha..."
Saam Ved  -    13-1462       Begins with "Tat Savitur Varenyam..."

How to do its Jaap
In the morning and in the afternoon Gaayatree Jaap should be done in standing position, while in the evening its Jaap should be done in sitting position. 1,000 times Jaap of Gaayatree Mantra is said to be the best, 100 times Jaap is considered medium, while 10 times Jaap is said to be ordinary. In the beginning Pranav (Aum), after that "Tat Savitur Varenyam..." - the three-line Mantra is to be used in Jaap.

Brahmchaaree, Vaanprasthee and Yati should use 6 Aum in this Mantra, or use 2 Aum - in the beginning and in the end of the Mantra; but a Grihasthee should use only 1 Aum - just in the beginning.

Illiterate persons who cannot utter Gaayatree Mantra can perform Panchaaksharee Gaayatree - "Om Bhoo Bhuvah Swaha". If they cannot utter even these words, they can perform the Jap of "Hari Om Tat Sat". This is also equal to Panchaaksharee Gaayatree Mantra.

Many More Gaayatree Mantra
The Rishi of the yore composed different Mantra on the same meter as that of Gaayatree on different manifestations of God. The names of 21 Devtaa of them are given below. These 21 Gaayatree Mantra are apart from the Vaidik Gaayatree Mantra - Om Tat Savitur Varenyam Bhargo Devasya Dheemahi Dhiyo Yo Nah Prachodayaat. See more Gayatri Mantra here

(1) Shiv,  (2) Ganesh,  (3) Narasinh,  (4) Naaraayan,  (5) Vishnu,  (6) Raam,  (7) Krishn,  (8) Brahmaa, (9) Hanumaan,  (10) Hansaa,  (11) Mahaalakshmee,  (12) Durgaa,  (13) Kaalee or Devee,  (14) Pushan,  (15) Kaam,  (16) Yam,  (17) Soorya,  (18) Agni,  (19) Varun,  (20) Indra,  (21) Sarp

(3) Gaayatree Devee
Gaayatree is a Devee also. She is said to be the mother of Ved. In the morning she is Brahmaa's power Gaayatree, in the afternoon she is Rudra's power Saavitree, and in the evening she is Vishnu's power Bhagavatee Saraswatee.

In the morning Gaayatree is Rig Ved form in a girl's form and she has four faces. Swan is her ride. In the afternoon she is Saavitree with three eyes wearing lion's skin. Doyaj Moon is in her matted locks and bull is her ride. In the evening she becomes Saraswatee, of dark complexion, wearing Peetaambar and her ride is Garud.

Gaayatree Mantra has three curses on it - from Vishwaamitra Jee, Vashhishth Jee and Brahmaa Jee. So after the Jaap of Gaayatree Mantra three Shaap Vimochan Mantra should be recited - "Vishwaamitra Kalp" book.