It was forged by the Huldra Brothers, Sindri and Brok, who also forged Thor's hammer, Mjölnir, after feeling responsible for the destruction brought about by Thor. As a weapon made to oppose the power of Mjölnir and inspired by the epic size of Jörmungandr, Brok suggests the axe be named Leviathan. According to Sindri when first meeting him, the blade was made for and given to Laufey who passed it on to her husband Kratos, before her death.
The axe has several runes inscribed on the blade that grants it different powers, among them the use of ice, and the ability to recall the weapon from any distance. It also has two slots for Runic Attacks to placed in, a heavy and light attack for each slot. The Axe Pommel is customizable with pommels found throughout the Realms or bought to Brok and Sindri.
During Kratos' journey to spread Faye's ashes, he encounters Brok and Sindri, who each upgrades the axe, improving its magic and attack strength. Upon bringing one of the brothers a Frozen Flame, the axe can be further upgraded, increasing the size of the blade and adding ornate gold to the blade and handle.
Wrath of Flame: Low Perk activation chance to grant Wrath of Flame on any successful hit. Wrath of Flame greatly increases Strength, restores a small amount of Health, and fires a wave of energy on normal attacks.
Get if from the Muspelheim Shop
Grip of Tanngiost
Fist of Thor: Low Perk activation chance to strike with an explosion of lightning that inflicts Shock damage to all nearby enemies on any successful axe hit.
Complete the Hammer Fall favor in Veithurgard
Hræzla Farmaðr’s Grip
Warrior’s Health Burst: Low Perk activation chance to grant a Health Burst on any successful axe hit.
Complete the Family Business favor.
Forbidden Grip of the Ages
Word of Ages: An ancient relic that increases all of Kratos’ Stats. Adds a concussive wave to the end of the R1 combo.
Obtain it after completing the Secret Caldera Realm Tear
Grip of the Maze
Cleansing Light: Very high Perk activation chance to restore some protection against the Cursed Mist of Niflheim on any successful kill. Passively grants resistance to the Cursed Mist.
The "Leviathan" is a sea monster mentioned in the Hebrew Bible and it has nothing to do with Nordic Mythology. According to Creative Director Cory Barlog, there's a reason why they chose that name.
The name Leviathan is strictly tied to the Judeo-Christian religions, so its use to describe the World Serpent is unusual.
It is speculated that this is related to the original ending David Jaffe intended for God of War III, where monotheism is established. In Barlog's words, "it's a name that […] is carried through-out history, so it might have some intersections with later parts of history, perhaps". This implies that monotheistic religions are actually inspired by the different mythological worlds.
Kratos can throw and call back the Leviathan similar to Thor's Mjölnir. This is not surprising considering both weapons were forged by Brok and Sindri.
The Leviathan is very rarely, if not never, mentioned by its name in the 2018 game. It is mostly referred simply as " axe" or "frost axe" by characters in the game. Similar case happens to the Blades of Chaos.
Cory Barlog said that he always wanted Kratos to wield an axe as his main weapon after the end of his Greek Era. He wanted him to be able to throw the axe, but during the alpha-stage it became a hassel for testers to have to pick up the axe from wherever they threw it to, creating the need to be able to recall it from anywhere like Thor could.
Brok and Sindri's brand bears resemblance to the Ingwaz rune (ᛝ).
While resting on Kratos' back, the Leviathan hangs from a hook that is shaped as the serpent-like Greek letter Omega, which has always been incorporated in the "God of War" titles' graphic.