There were various inquisitions over a period of nearly a thousand years. Most of them were based on the government of particular countries, to some extent or another with Church cooperation. They were court systems set up to examine various things - there was no set agenda from century to century. The most famous, the Spanish Inquisition, about which so much nonsense has been written, was mainly a government run inquiry into Muslim traitors in Spain. The Inquisition, itself, did very little, certainly nothing like "common wisdom" would have it with torture, etc. and was very limited in scope. For a good overview, pick up the book,
Seven Lies About Catholic History at the link below.