The First War Part 1
Perdiccas, the leading Diadoch at the time, was already betrothed to the daughter of Antipater, attempted to marry Alexander's sister, Cleopatra, a marriage which would have given him claim to the Macedonian throne. In 322 BC, Antipater, Craterus and Antigonus all formed a coalition against Perdiccas's growing power. Soon after, Antipater would send his army, under the command of Craterus, into Asia Minor.
In late 322 or early 321 BC, Ptolemy stole Alexander's body on its way to Macedonia and then joined the coalition. A force under Eumenes defeated Craterus at the battle of the Hellespont, however, Perdiccas was soon after murdered by his own generals Peithon, Seleucus, and Antigenes during his invasion of Egypt, after a failed attempt to cross the Nile. Ptolemy came to terms with Perdiccas' murderers, making Peithon and Arrhidaeus regents in Perdiccas's place, but soon these came to a new agreement with Antipater at the Treaty of Triparadisus. Antipater was made Regent of the Empire, and the two kings were moved to Macedon.
Antigonus was made Strategos of Asia and remained in charge of Phrygia, Lycia, and Pamphylia, to which was added Lycaonia. Ptolemy retained Egypt, Lysimachus retained Thrace, while the three murderers of Perdiccas—Seleucus, Peithon, and Antigenes—were given the provinces of Babylonia, Media, and Susiana respectively. Arrhidaeus, the former regent, received Hellespontine Phrygia. Antigonus was charged with the task of rooting out Perdiccas's former supporter, Eumenes. In effect, Antipater retained for himself control of Europe, while Antigonus, as Strategos of the East, held a similar position in Asia.
The First War Part 2
Following the opening stages of the first war of the Diadochi where the alliance headed by Antipater, Craterus and Ptolemy had fought against Perdiccas and those loyal to him, a new settlement had been reached at Triparadisus. Notably Antipater was to become Regent, and Antigonus Monopthalmus was appointed to campaign against Eumenes and the remainder of the of the pro-perdiccan faction. As the various parties departed from Triparadisus, it was time to make the settlement a reality.
Sources:
Ancient Sources:
Arrian Successors 1
Diodorus Siculus Library of History 18.16-40
Plutarch Eumenes
Modern Sources:
Anson, Edward M. Alexander's Heirs : The Age of the Successors, John Wiley & Sons, Incorporated, 2014.
Anson, Edward. “Ptolemy and the Destruction of the First Regency.” In Ptolemy I Soter, edited by Timothy Howe, 20–35. A Self-Made Man. Oxbow Books, 2018.
Anson, Edward M. “Diodorus and the Date of Triparadeisus.” The American Journal of Philology 107, no. 2 (1986): 208–217.
Errington, R. M. “From Babylon to Triparadeisos: 323-320 B.C.” The Journal of Hellenic Studies 90 (1970): 49–77. Erskine, A. (Ed.). (2003). A companion to the hellenistic world. John Wiley & Sons, Incorporated.
Hauben, Hans. “The First War of the Successors (321 B.c.): Chronological and Historical Problems.” Ancient Society 8 (1977): 85–120.