The Papal Inquisition is still with us, as the "Congregation for the Defence of the Faith" and still active in defending papal power; the Spanish Inquisition was a separate institution — an agency of the Spanish Government, not the Church — which was suppressed in 1834.
The Inquisition first began as a series of inquisitions, local enquiries conducted by bishops as to the local heretics, in particular the Albigensian Cathars (who not really heretics, but a separate religion all together). However, around 1230, a formal institution, the Inquisition, was established by the pope.
Over time, the Inquisition was successful in this task, and by the 1300s there were few and decreasing numbers of Cathars left to persecute. Like many institutions, the Inquisition found itself a new set of targets, maleficia, sorcerors and witches.
The Christian conquest of Spain in 1492 left their most Catholic Majesties, Ferdinand and Isabella with a problem, a culturally diverse population that was variusly Moslem, Jewish, Christian, and converts of varying degrees of sincerity. This led them in the same year to establish the Suprema y General Inquisitión as an agency of their government.
Burman provides a readable introduction to the history of the inquisition from its mediaeval beginnings to the present day. He provides memorable epitomies of the key features of each stage of the inquisition's history, showing how the institution changed over time.
Burman also describes the inquisition's trial of Galileo and suggests that the real reasons for his ordeal may have been the conflict between the institutional needs of the inquisition and Galileo's inflexibility, and also the difficuties that Galileo's atomic theories made for the doctrine of transubstatiation.
Burman ends by asking whether the inquisition was worth it. Did the inquisition preserve the Christian nature of Western Europe, and was it, therefore, ultimately justified?