Thudydides Book I Chapter 4

Recall that when we left Thucydides, Sparta (the Lacedaemonians) had just decided that they had to fight Athens. In this, they were motivated less by the entreaties of their Corinthian allies than by fear of Athen's growing power. Thucydides now turns to a flashback, recounting the events between the end of the war with the Medes, in which the two parties were allies, and the Congress of Lacedaemon, where the Spartans decided on war.

That period began with further joint action against the Medes, with Sparta still in the lead. The Spartan general Pausanias turned out to be such a jerk that the allies revolted and Athens took the lead:

Meanwhile Pausanias, son of Cleombrotus, was sent out
from Lacedaemon as commander-in-chief of the Hellenes,
with twenty ships from Peloponnese. With him sailed the
Athenians with thirty ships, and a number of the other
allies. They made an expedition against Cyprus and
subdued most of the island, and afterwards
against Byzantium, which was in the hands of the Medes,
and compelled it to surrender. This event took place
while the Spartans were still supreme. But the violence
of Pausanias had already begun to be disagreeable to the
Hellenes, particularly to the Ionians and the newly
liberated populations. These resorted to the Athenians
and requested them as their kinsmen to become their
leaders, and to stop any attempt at violence on the part
of Pausanias. The Athenians accepted their overtures,
and determined to put down any attempt of the kind and
to settle everything else as their interests might seem
to demand. In the meantime the Lacedaemonians recalled
Pausanias for an investigation of the reports which had
reached them. Manifold and grave accusations had been
brought against him by Hellenes arriving in Sparta;
and, to all appearance, there had been in him more of
the mimicry of a despot than of the attitude of a general.
As it happened, his recall came just at the time when the
hatred which he had inspired had induced the allies to
desert him, the soldiers from Peloponnese excepted,
and to range themselves by the side of the Athenians.

Might be time to recall GW.

After that, the Lacedaemonians went home and mostly minded their own business (whatever that may have been) while the Athenians built ships, fought wars, and endeavored to expand their empire. These enterprises were by no means uniformly successful. Egypt revolted against the Medean King, and Athens committed a large force of ships and men to the cause - ultimately, nearly all were lost. There were occasional conflicts between Athens and Sparta, but most stayed rather small scale, and there were long periods of truce.

If you want to follow the details of the battles, you will again need the very cool maps of Bernard Suzanne.