Abbadon is a Greater Demon from Hell. Faster than Shadowhunters, Abbadon is an Angel of Death, referred to as the Lord of the Fallen. Abbadon is listed among those angels who fell with Lucifer, referred to as the Ancients.
In 2007, Abbadon killed and possessed Madame Dorothea in her own apartment when she opened the Portal her mother had been protecting. He then hid the majority of its ethereal form just outside the Portal, making him undetectable by the Shadowhunters' Sensor.
When Clary Fray, Jace, Alec, and Isabelle Lightwood came to reclaim the Mortal Cup, the demon confronted the group, wanting the cup for himself to give to Valentine, and gravely injured Alec. Simon Lewis used Alec's bow and arrow to break the skylight, allowing sunlight to burn Abbadon, most likely sending him back to the Void.
Said to be at least nine feet tall, Abbadon slightly resembled a rotting human skeleton. He had livid and bruised-looking flesh, a misshapen head, a skull for its face, with caved-in holes for its eyes and a nose, two rows of jagged glass-sharp teeth, and black, cracked, and filthy bones that looked as if he was rotting and ancient. His taloned fingers were stripped and skeletal, his thin-fleshed arms pocked with oozing black sores through which more yellowing bone was visible. His hide was grey, with things seemingly crawling inside of it.