The Holy Inquisition is an institution within the Church of Titanius with the official aims of combatting heresy, purging lands belonging to the Church of demons and undead alike, curbing corruption within the Church.
Precursors to the Inquisition have existed in Froturn for almost as long as the state itself did, in two forms: a group of church judges, armed with the right to question people involved in eccelestial affairs - and then to be either jduged as guilty and excommunicated (and very often executed or imprisoned afterwards) or deemed innocent and let go; and various short-lived movements within the Church to promote orthodoxy and curb both corruption and heterodoxy within the Church. During Froturn's dark period of instability 1100-900 BEKE, several heretical movements managed to flourish, only to find all their followers burned on a stake when royal power was consolidated in the 9th century BEKE.
Heretical movements and heretical preachers would still show up occasionally, and as expected, nearly all of them found themselves silenced one way or another - burned on a stake or exiled. However, until the Kingdom of Etrand was founded, there was no named, organized and long-lasting institution that was armed and geared up for perpetual warfare against infidels within the borders.
The Holy Inquisition was founded by King Corlagon I of Etrand - although precursor have already existed in the Kingdom of Froturn -, with the goal of eradicating the last of those pagans who were unwillign to convert to the new religion. The Holy Inquisition was a very drastic but overall effective solution to the problem. At the time, the number of Inquisitors was few, and they were mostly wise men, armed with strong magical powers to demonstrate how powerful the Church is, preaching to the last pagans that the Old Gods are dead and anyone following them will join them. However, during Corlagon's reign, the Church still did not manage to claim all of the population for itself, as paganism has managed to survive in the underground despite the best efforts of the Inquisition, and even many of the military and nobility were still crypto-pagans, still inclined towards the old religion.
After the death of Corlagon, his successor Symon has made up his mind to invest much more money into the Inquisition. He also greatly expanded their numbers. Rather than recruiting "wise men", he started recruiting among fanatics. He took in the fanatics, and ordered the previous generation of Inquisitors to train them how to use magic and maces alike. With that, he created the Inquisition we know today.
The Inquisition's new tactic of turning ignorant fanatics into the arm of the church - Inquisitors - has turned out to be a very effective way to fight back heresy and paganism alike.
Thanks to KIng Symon's efforts, all remnants of the old faith have disappeared within the Kingdom of Etrand, with pagans either fleeing to Hulra or being found by the Inquisition and executed in various ways. After this, Symon believed that the Inquisition's work was done. It is a common historical misconception that Symon disbanded the Inquisition - he simply reduced their numbers, letting a large number of them retire to live peaceful lives as monks.
However, that did not last forever. as trouble showed up its head again during the reign of King Hereric, the first necromancers and vampires began appearing. King Hereric employed the Inquisition to get rid of this new menace, but their strength did not seem enough - which is why he turned to the knights. After finally expelling them, the Inquisition was put to rest for another two years. Hereric would use the Inquisition once again in his attempt to retake the throne by using trumped-up charges of heresy against him. It did not work, and instead, his very own order of Knights was the institution that restored him to the throne. After Hereric was restored to the throne, he once again put the Inquisition to rest.
Andrei's Inquisition was different from the previous ones. Previously, the Inquisition's job - other than fighting abominations such as undead and demons - was to find and round up people suspected of heresy, and then the secular authorities would either have the persons executed, or turn the case over to the Church to judge. However, Andrei's Inquisition had much more authority and autonomy, and it had the right to judge a person and execute him/her.
After the demon-worshipping cults were mopped up, the Inquisition was reassigned to be under the control of the Church of Ttanius, rather than the secular authorities of the Kingdom of Etrand.
Many saw this as a beginning of the corruption of the Church of Titanius, as High Elves and Humans would begin using the Inquisition for their own gains, they would bribe the Inquisition and have people threatening their power base silenced. That is how the Inquisition has earned the dubious reputation it has today. Rather than fighting corruption within the Church, they started perpetuating it.
King Hereric II too strengthened the Inquisition by donations, and urged it to nip reformist movements and rebellions in the bud. However, the massacres of innocents, news of torture and other atrocities attributed to the Inquisition did not remain a secret from the general populace for long, and as a response, the more determined organized into underground "exile groups" - social clubs for heretics who wanted a community that would help them live safely, away from the ever-vigilant eyes of the Inquistion.
After that, the flames of Inquisition and the burning of people on stakes became something that could happen anywhere. The most famous "exile group" (heterodox Titanist religious movement) is the Order of the Eternal Crystal Flower. They are the most widely known infamous group of heretics that has managed to evade the Inquisition nearly every time, having their own secret base in an unknown location where the Inquisition has so far failed to locate it.