Shirou Emiya 1st
Authorities
Gilgamesh:
Gate of Babylon King Gilgamesh treasury with all the divine artifacts and treasures money food anything he needed it was there
Heracles:
Nine lives a technique made by Hercules which was passed down as an authority performing 9 successful slashes against the opponent that looks like one swing.
12 lives have to be killed 12 separate times to actually be dead as well as each time killed Gaines immunity for what killed him last.
Hephaestus:
Master of forge grants the user the ability to use any material to make any weapon or item.
Issei Hyoudou 2nd
verethragna:
10 incarnations
The warrior
The bull
The raptor
The white stallion
The boar
The camel
The ram
The goat
The Gale
The youth
Sun wukong:
ruyi jingu bang
nimbus
susanoo:
ame no murakumo no tsurugi copying authority for one time use
Arata Kasuga 3rd
Solomon:
Master of magic allows him to copy or master any spell and also allows him to make any magic he needs.
Seven deadly sins: has defeated all seven princes of hell
Pride to copy any spell or technique, ability.
Wrath allows him to counter any thing thrown at him with double impact be it magic or physical.
Greed allows him to steal his opponent's strength and add it to his own.
Sloth allows him to be able to make damage multiply from scratch to a major slash.
Gluttony as long as she has an ounce of magic can be generated infinitely.
Envy allows him to use the ability of alchemy turning coal from gold silver to water.
Lust let him use some of the ability of manipulating memories and emotions.
Kirigaya Kazuto 4th
Lancelot:
Master of arms allows him to use the ability of any weapon to their full capacity
arondight can transform itself into a mist around its user allowing it to be used in the form of any weapon from a stick to a piece of wood all are infused with it.
Gawain:
Sunrise when the sun is rising and setting his power is amplified times 10 for each moment of the sun is up and at noon is power becomes 100 times for 1 minute.
Excalibur Galatine The sword gains energy when it's in the Sun and is amplified when using sunrise to sharpen its edge and it contains all the energy until it's used to empower the user as well.
Charlemagne:
Joyeuse A powerful secret sword that generates its own energy as well as able to perform magic as a wand.
Holy empire grandson the ability of using the 12 knights of Charlemagne it's weapons as its own joyeuse can transform into any weapon of the 12 knights
Jaune Arc 5th
Zeus:
King of the skies allows him to use lightning as well as some in hurricanes as well as let him fly.
The court grants him the ability to impose someone with one authority of his own.
Poseidon:
King of the seas Grantham the ability to manipulate the ocean
Sieg:
Sigurd or Siegfried but both are considered
Gram a sword with seven daggers that can cut through any material in the world
Balmung once an enemy is hurt it boosts leaves there abilities by 30%
The indestructible body cannot be damaged by anything.
Wisdom by looking at something he can gain information and its weaknesses