Summons - Final Fantasy XIII
Shiva in a historical context:
Shiva, referred as both male and female in various scriptures, is most well
known as the Hindu god of destruction and trasnformation.
Shiva is most often seen in meditation or as a skilled dancer.
The Shaivism denomination of hinduism considers Shiva to
be the supreme god, while other denominations consider
her to be merely a highly ranking diety. The sanskrit word
“shivam” is most likely defined as favorable, gracious, and
friendly.
SHIVA
The Diamond Dust Returns
Shiva was one of the first summons to be shown off along
with the unveiling of Final Fantasy XIII during E3 2006.
She was the source of much confusion as she, for the first
time, took the form of two sisters, one light and one dark,
who appear to merge to create a motorbike, harping back
to the days of the classic motorcycle minigame in Final
Fantasy VII. It is believed that Shiva will likely have some
sort of function outside of battle, as hinted by developer
statements that summons would take on a “digital” form
in Final Fantasy XIII, and by more recent trailers that show
Mr. 33CM riding Shiva in her motorbike form as he tries
to rescue Lightning.
Shiva in the Final Fantasy Series:
Shiva was among the first summons to be introduced in the series with
the release of Final Fantasy III, and since then, has been
featured in every main Final Fantasy installment. Shiva
has primarily dealt Ice element damage, and is likely the
most well known female Final Fantasy summon, usually 
appearing as a beautiful, majestic young woman. Her
special ability is known as “Diamond Dust”, in which she
creates an arctic, chilly blast which devastates her enemies.
Siren in a historical context:
The sirens are most widely equated with Greek mythology as a trio of winged women seen near rocky coastal cliffs. They were said to produce an attractive, enchanting, and magnetic hymn with their combined played music and eloquent voices, which lured passerby seamen towards them. However, these seductions would prove to merely be a trap, aiming to shipwreck and kill the sailors.
SIREN
Deadly Beauty
Siren was first unveiled in the January 2008 issue of Shonen Jump along with Ifrit and Carbuncle. Other then her mystical appearance and angelic demeanor, not much is known about her role in Final Fantasy XIII. Similar to previous installments in the series, she is seen playing her harp while on what appears to be a watery surface, making it a reasonable conclusion that her attacks and status effect inducing magic will be 
similar to earlier games. However, unlike Carbuncle and Shiva, it is unknown what type of technological device she is summoned from or can transform into, or whether she has one at all.
Siren in the Final Fantasy Series:
Siren first appeared as a boss in Final Fantasy V, which viciously used spells such as sleep and silence on the hero's party. Since then however, she has reappeared as a summon in Final Fantasy VI and, more recently, Final Fantasy VIII, in which her special attack was known as Silent Voice. 
She usually deals minor physical attacks as well as magical status spells, most frequent of which is silence. The character of Siren is generally portrayed with angelic wings as well as a very revealing attire.
Carbuncle in a historical context:
Carbuncle is most commonly reffered to in mytholgy as an unknown, mysterious creature thought to be seen by the Spanish Conquistadors during the time of American Colonization during the 1700's. Whether this animal existed or not is unknown, the only thing known of 
the animal is that it was very small with some kind of bright object on its head. Multiple people have searched for this creature but to no avail. Carbuncle is also a name given to any sort of deep red gemstone.
CARBUNCLE
Woof Woof!
Carbuncle, like Siren and Ifrit, was first unveiled to the public in the January 2008 issue of Shonen Jump Magazine, as well as via a trailer to a private audience during Jump Festa 08’. To the surprise of fans everywhere, Carbuncle takes the form of a small puppy dog wearing what appears to be a clown’s outfit in Final Fantasy XIII. However, it continues to bear the red jewel that it is known for on the top of its head. 
Carbuncle takes the form of and is summoned from a CD [Compact Disc], or perhaps even a Blu Ray disc! In the Jump Festa 08’ trailer, a giant, floating, unknown, spherical object spews out hundreds of these discs, one of which is picked up by pigtails girl, who summons Carbuncle and seems to like it. Carbuncle will clearly play some sort of outside battle role in the game.
Carbuncle in the Final Fantasy Series:
Carbuncle has appeared in Final Fantasy V, VI, VII, IX, and XI in various forms, but is always a four-legged, cute and fluffy creature with a large red gemstone adorned on it
s head. Carbuncle’s Ruby Light attack does not attack the enemy, but rather boosts the party’s might with various status increasing magic, most notably but not limited to the reflect spell Reflect.
Ifrit in a historical context:
The name Ifrit comes from Arabic and Islamic Mythology. The Ifrit, also called efreet, ifreet, afrit, afreet, are a class of powerful jinn (otherwise known as Djinn, or Genie) that are said in the Quran to be among the creatures created by God (the others being Angels and Humans). Jinn differ from angels in that, like humans, they have free will, and they differ from humans in that instead of clay and blood, they are made of and bleed fire. 
However, normal humans do not have the ability to see the Jinn, and Ifrit’s especially consider themselves to be above all other creatures, because they were the first to be born into this world. Because of this, it is said Ifrit will seldom come to any creature’s aid.
IFRIT
The Spawn from Hell
To the delight of many fans, Ifrit was revealed alongside other summons in early January 2008. The fiery beast from hell has been confirmed to be returning in Final Fantasy XIII, 
however, little to none about his role in the game has been revealed. What remains certain however, is that he has a much more beastlike appearance, and will continue to be the series’ main fire elemental summon.
Ifrit in the Final Fantasy Series:
Like Shiva, Ifrit has become a mascot symbol synonymous with the series. Since his introduction in Final Fantasy III, he has appeared in almost every entry is some way, shape, or form as the fire elemental summon. His trademark move has been Hellfire, in which he spawns flames from the underworld to scorch his enemies ablaze. 
Ifrit has always been portrayed as a fiery demon, and is usually characterized by a malicious attitude and a strong dislike towards humans. He has been at the forefront of the series for a long time, some might not consider a game to be Final Fantasy without him.
