Chaldea’s history
So here's a quick recap of essential info of FGO: Chaldea is an organization created by Marisbury Animusphere: the director of Chaldea and father of Olga Animusphere.
In order for Chaldea to flourish, Marisbury participated in the Fuyuki Holy Grail War and won, getting his wish granted and thus received great fortune, enough to sustain chaldea
At some point of time Marisbury died of unknown circumstances, passing the title of director to his daughter Olga and most of his responsibilities to his advisor Lev Lainur
Now that Chaldea is officially funded and up and running they began developing different technologies
The first one was the lens SHEBA, capable of observing the past, present and future of human history, later on they developed technology capable of “Rayshifting” people into past eras
The second was the Fate system which is used to summon servants without the aid of the Greater Grail. The third servant to be successfully summoned was Da Vinci. Later on the FATE system would have been used to summon servants for the Masters of Chaldea
Thirdly they initiated a project to create a human-servant hybrid called Demi-Servants, basically a human capable of utilizing the powers and abilities of Heroic Spirits, unlike Pseudo-Servants which are humans that become the host for an heroic spirit, the heroic spirit taking control of the body of the host (for example: Ishtar and Jaguarman are pseudo-servants)
The only successful Demi-servant created was Mashu Kyrielight, who as a Demi-Servants suffers from an extremely shortened lifespan, with a limit of 18 years of life expectancy and she’s currently 16-17, meaning that death is near for her
In exchange for her short life span she became able to use the abilities of a Knight of the Round Table: Galahad, being able to use his abilities, shield and noble phantasm

Prologue of Fate/Grand Order
Chaldea with the lens of SHEBA learned that human history stopped at the beginning of the year 2016
Thus to combat this unknown threat they assembled 48 Master candidates to rayshift into the newly created unknown space, later on known as Singularity Fuyuki
Before Olga (the current director of Chaldea) is able to order the dispatchment of Chaldea’s masters an unknown explosion occurs on Chaldea, fatally wounding almost all masters and putting them in cryostasis, leaving Gudao/ Fujimaru Ritsuka as the only capable Master within Chaldea: The last master of humanity
With a team of Fujimaru, Mashu and Olga, and the support of Dr. Romani and Da Vinci they venture into the Singularity, where they learned that the bombing attack was caused by Lev Lanur, who has betrayed Chaldea and shows his true identity as Forneus, one of the Demon pillars under the command of the Mage King: Solomon. After the Lev “kills” Olga
The objective of Solomon is to incinerate human history/order (basically wipe out humans) and to do so he has placed holy grails at different key points of human history so they go off course of the recorded history and break the foundation of human history
Thse key points which became Singularities are:
2004.AD Fuyuki
1431.AD Orleans
60.AD Septem
1573.AD Okeanos
1888.AD London
1783.AD E Pluribus Unum
1273.AD Camelot
2655.BC Babylonia
With a heavy damaged Chaldea the only personnel capable of dealing with the situation are: Fujimaru, Mashu, Dr. Romani. Da Vinci, Fou-kun and unnamed Chaldea staff

Important characters:
Guda/Fujimaru Ritsuka: The last Master of humanity, his capabilities as a mage are atrocious yet was able to become a master thanks to his disposition of Rayshifthing
Mash Kyrielight: A Demi-Servants of the unique Shielder Class, Capable of using the abilities of Galahad, a legendary knight of the Round Table from the Arthurian legends. She has spent most of her life within Chaldea, knowing little about the outside world she views Guda/Fujimaru as her “Senpai” because of it and ought to learn from him
Romani Ackerman: The head of the medical facility of Chaldea, he became the director of a Chaldea after Olga’s death, known as a relaxed and calm person
Da Vinci: The third servant summoned with the FATE System. Originally a man during life he tinkered with his Saint Graph to take up the appearance of his masterpiece: The Mona Lisa. The reason for this is that Da Vinci wishes to be the embodiment of Beauty
Fou-Kun: a mysterious animal that resides in Chaldea, not much is known about it apart that it has some connection to the flower mage: Merlin
Solomon: The Mage King and Founder of modern magecraft, his objective is the incineration of Human Order/History, has a strong hatred against humanity

Terminology:
Master: A Magus that has formed a contract with an Heroic Spirit. Has 3 command seals capable of giving “absolute” orders to their servants
Servant: Legendary figures of history brought back a summoning ritual. Classified into seven standard classes and six irregular one: Saber, Archer, Lancer, Rider, Caster, Assassin, Berserker | Ruler, Avenger, Shielder, Moon cancer, Alter Ego, Foreigner
Demi-Servants : Humans capable of acquiring the abilities of Heroic Spirits and retain their own ego
Pseudo-Servants: Heroic Spirits that under usual circumstances are unable to be summoned by various reasons (mainly because their rank in “Divinity” is too high to be contained in a servant vessel) they opt to using living humans as their vessels, decreasing their power and merging their personalities with that of the host
Grand Servant: Servants summoned in a much greater vessel than normal servants, summoned by the “Counter Force” to combat “Beasts”. Only those who have reached the pinnacle of their servant class are qualified to be summoned as Grand
Counter force: the will of Alaya (humanity) or Gaia (The Earth) that puts agents of their choosing (or empowers certain people) to ensure that a desired outcome for Alaya or Gaia happens, Alaya and Gaia do not exists in harmony and can be on opposite sites, for example if Gaia declares humanity as a liability for the Earth it will try to eradicate humanity
Saint Graph: “The Core” of a Servants body
Living  People: Living Humans that somehow have gained a servant state
Grand order: the foundation of the world, obeyed the recorder history of humanity
Singularity: irregularities created in quantum-time lock points of human history, deteriorating the foundation of the Grand order to be able to archive the incineration of the world
Quantum-Time Lock: Key moments in the world’s history, their alteration affects the stability of the world making it to be eventually the culling of that world