The Classical Period started at the end of the second Persian invasion of Greece in 480 BC and finished with the death of Alexander the Great in 323 BC.
Much of the early defining politics, architecture, sculpture, scientific thought, theatre, literature and philosophy of Western civilization derives from Classical Greece, which was adopted by the Roman Empire and then passed down to us.

Click Here for the Timeline of Ancient Greece
In 480 BC, Xerxes, the son and successor of Darius, sent a more powerful army by land, with the navy in support, across a double pontoon bridge over the Hellespont. The Persians quickly conquered Thrace, Thessaly and Boeotia. Leonidas and his 300 Spartans delayed the Persians at the Battle of Thermopylae but were ultimately killed. Xerxes then advanced into Attica and captured and burned Athens, which had been abondoned by the Athenians. The subsequent Battle of Artemisium resulted in the capture of Euboea, bringing most of mainland Greece north of the Isthmus of Corinth under Persian control. However, under the command of Themistocles, the Greeks defeated the Persian fleet at the Battle of Salamis. Then in 479 BC, they defeated the Persian army at the Battle of Plataea.
The Delian League, which was an association of Greek city-states under the leadership of Athens, was founded in 478 BC, whose purpose was to continue fighting the Persian Empire after the Greek victory in the Battle of Plataea. However, it became apparent quite quickly that the League was a front for Athenian dominance over the Aegean. By 431 BC, the threat the League presented to Spartan dominace combined with Athens’ control of the Delian League prompted the outbreak of the Peloponnesian War.

The Peloponnesian War lasted from 431 to 404 BC fought between Athens and Sparta with their respective allies for dominance over the Greece. The war remained undecided for a long time until the decisive intervention of the Persian Empire in support of Sparta. Led by Lysander, the Spartan fleet finally defeated Athens, which allowed Sparta to dominate Greece for a period of time. There were three phases to this war: the Archidamian War (431-421 BC), which entailed king Archidamus II of Sparta invading Attica but being thwarted by the Long Walls of Athens and the Athenian fleet raiding Spartan territory, the Sicilian Expedition (415-413 BC), during which Athens lost almost all its navy in the attempted capture of Syracuse, an ally in Sparta, and the Ionian War (413-404 BC), in which the Spartans built a large navy and won a number of naval victories in the Aegean.

In 359 BC, Philip II became king of Macedonia and within the span of just 25 years the Kingdom of Macedonia came to dominate Classical Greece. This was done through diplomacy, marriage alliances and the improvements made to the Macedonian army, making it the most effective force in Greece at that time. In 338 BC, Philip gained dominace over Greece at the Battle of Chaeronea. He then created the League of Corinth, which brought Greek city-states into a formal alliance with Macedonia. The League had planned on an invasion of Persia but Philip II was assassinated in 336 BC before this could happen. He was succeeded by his son Alexander the Great.
In 334 BC, Alexander the Great invaded the Persian Empire and conducted a series of campaigns that lasted for 10 years. Having conquered Asia Minor, he broke the power of Persia in a series of decisive battles, including those at Issus and Gaugamela, and annexed the Persian Empire. Now the Macedonian Empire held a vast swath of territory from the Adriatic Sea to the Indus River. However Alexander wanted to push further East and so invaded India in 326 BC. Due to the demand of his homesick troops, he eventually turned back and later died in 323 BC in Babylon.

In the years following his death, a series of civil wars broke out across the Macedonian Empire as his generals broke apart his empire to form their own kingdoms, known as the Wars of the Diadochi.