Originally a Phoenician goddess of lasciviousness, equivalent of Babylonian Ishtar
"The Twenty-ninth Spirit is Astaroth. He is a Mighty, Strong Duke, and appeareth in the Form of an hurtful Angel riding on an Infernal Beast like a Dragon, and carrying in his right hand a Viper. Thou must in no wise let him approach too near unto thee, lest he do thee damage by his Noisome Breath. Wherefore the Magician must hold the Magical Ring near his face, and that will defend him. He giveth true answers of things Past, Present, and to Come, and can discover all Secrets. He will declare wittingly how the Spirits fell, if desired, and the reason of his own fall. He can make men wonderfully knowing in all Liberal Sciences. He ruleth 40 Legions of Spirits" Ars Goetia
Referred to in The Lesser Key of Solomon as a very powerful demon. The Lesser Key of Solomon contains detailed descriptions of spirits and the conjurations needed to evoke and oblige them to do the will of the conjurer (referred to as the "exorcist"). It details the protective signs and rituals to be performed, the actions necessary to prevent the spirits from gaining control, the preparations prior to the invocations, and instructions on how to make the necessary instruments for the execution of these rituals.
The name "Astaroth" as a male demon is first known from The Book of Abramelin in 1458.
Sebastien Michaelis who was a French inquisitor and prior of the Dominican order who lived during the late 16th and early 17th centuries who's notable co authored book Histoire admirable de la possession d'une penitente contained a classification of demons who's names where named in a case he was involved in in 1612 involving several nuns.
Astaroth according to Sebastien Michaelis is a demon of the First Hierarchy, who seduces by means of laziness, vanity, and rationalized philosophies. His adversary is St. Bartholomew, who can protect against him for he has resisted Astaroth's temptations. To others, he teaches mathematical sciences and handicrafts, can make men invisible and lead them to hidden treasures, and answers every question formulated to him. He was also said to give to mortal beings the power over serpents.
In art, in the Dictionnaire Infernal, Astaroth is depicted as a nude man with feathered wings, wearing a crown, holding a serpent in one hand, and riding a beast with dragon-like wings and a serpent-like tail.