Official Canon Edit
Abaddon was originally the First Captain of the Sons of Horus, having fought many battles in the Horus Heresy. When Horus was defeated at the Siege of Terra, though, the Traitor forces retreated into the Eye of Terror. With the legion now broken and without a leader, many broke off into other war bands until Abaddon reformed the Sons of Horus into the Black Legion, and cemented his leadership by launching the first Black Crusade.
There have been thirteen Black Crusades in total; originally they were all attempts to seize Cadia, the only secure way out of the Eye of Terror, but this has since been retconned. Each Crusade was a separate operation with its own goals; in the twelfth Black Crusade, Abbadon obtained the Blackstone Fortresses, which he used in the thirteenth Black Crusade to smash Cadia's pylon network and allow the Eye of Terror to expand. His ultimate goal is to eventually reach Terra and finish what his father started by killing the Emperor.
TTS Canon Edit
Abaddon had Fulgrim call up Lucius the Eternal to tell him that he was "having another one of his huge parties,” meaning the thirteenth Black Crusade. Eldrad Ulthran saw Abaddon and his Crusade in a vision, and was forced to contact Asdrubael Vect to warm him of the impending war.