The end of the Peloponnesian War ushered in a, rather ill fated, period of Spartan political dominance. As an elitist warrior society, the Spartans proved quite ill-suited to this role, and relied on military (particularly naval) dominance in order to maintain their status. Sparta's political structure eventually crumbled under the increased diplomatic and bureaucratic weight, leading to the fall of Sparta.

The Peloponnesian War was fought between Athens (and their allies) and Sparta (and their allies). It was fought from 431 - 404 BCE. The war ended in total defeat for the city-state of Athens and the loss of her empire. It also greatly weakened the Greek city-states in general, including Sparta, and ushered in the opportunity for the rise of Macedonia under Philip and Alexander the Great.

The First Greco-Persian War broke out as a result of Athens lending their support to the Ionian Revolt. The Ionian Greeks had been conquered by the Persian Empire, much to the dismay of their fellow Greeks in Athens and elsewhere. When the Ionian Greeks revolted against their Persian masters, Athens (and other city-states) sent troops to help the rebellion. These troops contributed to the destruction of the Persian city of Sardis. This prompted the Persian Emperor, Darius I, to vow that he would conquer Greece and destroy Athens.

The Battle of Thermopylae featured the last stand of King Leonidas during the Second Persian Invasion and is one of the most famous in history, making this answer the best choice. The Battle of Marathon brought the First Persian Invasion to a halt but was not a part of the Second, so it would not be a good choice. The Punic Wars were a series of wars fought between Rome and Carthage and did not involve Greece or Persia, so that would not be a good choice. The Battle of the Bulge and the Battle of Waterloo were both famous battles that happened thousands of years after the event in question, so they would not be good answers either.

The Battle of Marathon was fought between the forces of Athens and the Persian Empire in 490 BCE. It was the decisive battle of the First Greco-Persian War and ended in victory for the Athenians. It brought to an end the first attempt by the Persian Empire to conquer the Greek mainland.

The Persian Emperor during the Second Greco-Persian War was Xerxes. Xerxes led an invasion of the Greek mainland during the fifth century BCE. It is during this invasion that the famous Spartan stand at Thermopylae took place. The war ended with the complete destruction of the Persian fleet at the Battle of Salamis.

Lysander was the most influential and notable Spartan admiral during the Peloponnesian War. He led the Spartan forces to victory over the Athenian navy and soon thereafter forced the complete capitulation of the city of Athens.

Themistocles was a renowned politician and general in Athens during the Athenian Golden Age. He was one of the most influential politicians during the Greco-Persian Wars. He is responsible for increasing the size of the Athenian navy and for leading the Athenian navy in the pivotal Battle of Salamis. It was due to his foresight and leadership that the Persian navy was defeated and Greece was preserved.

The Delian League was led by Athens. The Delian League was formed in 477 BCE, in the wake of the second Persian invasion of Greece. It was an organization of city-states, under the direction of Athens, who came together to provide for mutual protection against future Persian invasions. The league, however, quickly devolved into an expression of Athens’ personal power which led to many conflicts within the league. It also led to the rise of the Peloponnesian League, led by Sparta, and the outbreak of the devastating Peloponnesian War.

In the aftermath of the Persian Wars, the city-state of Athens suddenly found itself in a position of unrivalled power in the Aegean and the rest of the Greek-speaking world. Athens, using its position as the head of the Delian League, was able to create something of an empire in a very short space of time. However, the Athenian Empire would last less than a century before it was torn down by the Spartans in the Peloponnesian War.