Demonology is the systematic of demons. Insofar as it involves exegesis, demonology is an orthodox branch of theology.
Christian demonology
The most extensive exposition of Christian demonology are Heinrich Kramer's Malleus Maleficarum—once thought to have been co-written by Jacob Sprenger— and Nicholas Remy's Demonolatry, both assuming the reality of witchcraft and its capability of posing a threat to the Roman Catholic church.
Demonology refers to catalogues that attempt to name and set a hierarchy to demons and spirits thought to be malignant. In this sense, demonology can be seen as the mirror image of angelology, which attempts to compile the same information for good spirits.
In Christian tradition, demons are fallen angels, so demonology could be considered a branch of angelology. The grimoires of occult magic are the tomes that contain the lore of this version of demonology, containing instructions on how to summon them and bend them to the conjuror's will, yet not all occultists modern and ancient necessarily evoked demons.
It is somewhat unclear how many angels were actually engaged in the war in Heaven and the exact number of the host is open to conjecture for many.
In the 15th century though it was estimated that 133,306,668 angels fell from the Heavens in a total of 9 days according to the Bishop of Tusculum (c. 1273), and this was reaffirmed by Alphonso de Spina (c. 1460).