The Azure Prophecy
There are several known passages of the Azure Prophecy:
When the time begins its march time anew, they shall return as visitors: Jiants from the Hills of a world not our own. Upon Grymoire, they will wreak two divergent futures: one that brings salvation; and the other, ruin—an enigma to confound even the highest mind.A fragment learned from Princess Sarah.
Again, it shall be Ragnarok—a battle...initiated by new Champions, and yet...to whose salvation?A fragment learned from Yuna
The Azure Prophecy was written by the First Summoner, while the Crimson Prophecy came around later.
The Azure Prophecy is first mentioned by Princess Sarah at Cornelia when she speaks that Lann and Reynn are "the stuff of prophecies" and reveals its words to them. Later, after Yuna tells the twins about the Heralds and advises them to go to Saronia Harbor, she speaks to herself of another part of the Prophecy.
The Crimson Prophecy is first mentioned, although by a more general term "prophecy", by Faris on her ship. As she is unable to recall what it says exactly she asks her moogle companion Mog, who remembers it, who says that the prophecy says that "Jiants from the Hills will collect four keys, open up a pathway to the Crystal Tower, brave its dangers, and mount the very heavens". The moogle also recalls a vague hint towards the first of the keys: a valley of fire, and Faris advises the twins to search in the Babil Region.
After Lann and Reynn awaken Tifa at Dragon Scars, the Plumed Knight and the Masked Woman ponder about the Azure and Crimson Prophecies, with the Plumed Knight saying that the latter one must be completed as soon as possible.
At the town of Nibelheim, the twins learn from Rydia, a young summoner who researches the Crimson Prophecy, that the prophecy mentioned by Faris is known as "the Crimson Prophecy" with "the Azure Prophecy" being the first one. She reveals that the Azure Prophecy in its original form speaks of four sigils, but says nothing about four keys like the Crimson Prophecy does, and calls the original prophecy "much more abstract". Rydia then states that according to her research the "valley of fire" from the Crimson Prophecy is likely Valley Seven and together with the twins they go there.
The Crimson Prophecy is eventually revealed to be a complete lie, fabricated by Segwarides specifically to manipulate the twins into opening the Ultima Gate and unleashing the Cogna.