The Burning Times are what Witches call the Inquisition. Google it for exact dates. Many of the people tortured and murdered during the Burning Times were not Witches at all, but people whose neighbors had a grudge with them, or wanted their land, or wanted a quick bit of coinage (people were rewarded monetarily for turning in Witches). In many cases, they were old women that society no longer deemed "useful" and it was an easy way to get rid of them. Cats were also severely persecuted during this time, and in Europe the housecat nearly became extinct because so many were killed. This helped the black plague spread, since rats spread the plague and there were no cats to kill the rats. It was the Catholics who conducted this, and it was done in the name of God and rooting out heretics.
It was very easy to label someone a Witch and then find "proof" to back it up. Often owning a cat was enough proof that you were consorting with Satan, and since many old women had cats (for company and to keep mice away) that was all the proof many people needed. And since there was very little understanding of medical issues, if someone said, "I hope your cow dies!" to a neighbor during an argument and then the cow coincidentally died, that was all that was needed to prove the person was a Witch. Birthmarks, moles, and other skin abnormalities were proof that you consorted with the devil as well.
Witch hunts did continue through England for several centuries after the Inquisition officially ended, and of course there were the Salem Witch Trials in the U.S., which started because a reverend's daughter was seized by "fits of hysteria", for lack of a better term. She attributed this to the devil and started accusing townsfolk left and right. Interestingly enough, two generations later a minister was seized by the same fits, declared they were because of God, and started the Revivalist movement that still exists today, where people sway and shake because they're apparently possessed by the lord.
Look up Malleus Maleficarum if you want an idea of what the criteria was for identifying and dispatching Witches.
Bright blessings.
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