Pope John Calvin: the last Pope, moved the seat of Papacy to Geneva and set up the Consistorial Court of Discipline, establishing the absolute authority of the Church.

The Church: the major religious power of Lyra's world, administrated by the Consistorial Court of Discipline through a tangled framework of colleges, councils, and lesser courts.

Consistorial Court of Discipline:
the disciplinary arm of the Magisterium, it is the Court's duty to investigate acts of heresy and exact punishment against those found guilty.  Although both the Society and the Court act in the interest of the the Church, they are competitive and attempt to keep their discoveries secret from each other and from the other branches of the Magisterium.

College of Bishops: where most of the Church's power lay in the century prior to Lyra's birth until the Consistorial Court of Discipline became the most active and feared part of the Magisterium.

The Magisterium:
the tangle of courts, colleges, and councils that replaced the Papacy to control the Church after the death of Pope John Calvin.

Oblation Board:
a semi-private organization run by an enemy of Lord Asriel's.  The Oblation Board is not entirely answerable to the Church's Consistorial Court of Discipline, but instead appears to operate outside normal constraints, and now seems to be gaining power.

The Society of the Work of the Holy Spirit:
the research arm of the Magisterium that tests and classifies heretical speculation.  Members of the Society are sworn to poverty and chastity, but not to obedience, as it is necessary to their work that speculation be allowed.
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Phillip Pullman