The Achaemenid Empire is also known as the First Persian Empire. Based in what is now Iran, it ruled over a vast expanse of western Asia, southern Europe, and northern Africa in the period between 550 and 330 BCE.
Cyrus the Great founded the Achaemenid Empire in 550 BCE after conquering the Median Confederation. He would go on to defeat the Lydians and Babylonians, famously freeing the Jewish people from their Babylonian captivity along the way. Cyrus began the process of creating a highly-centralized, multi-ethnic state, and his successors continued to build upon this foundation.
The Achaemenid Empire used various languages to rule over its many peoples, but around 500 BCE it began to use Aramaic as its lingua franca. The various sections of the empire were tied together not only by this language, but also by improved roads and a type of postal service. Although the rulers were Zoroastrian, they practiced religious tolerance and allowed their subjects to continue to worship in their own ways. This tolerance is evident in Cyrus's orders to allow the Jewish people to build their Second Temple in Jerusalem. Later, Darius the Great would even order the Achaemenid treasury to pay for completion of the temple.
Cyrus's son Cambyses II managed to conquer Egypt in 525 BCE, but died three years later on his way back to Persia. A pretender called Gaumata, claiming to be Cambyses's brother, seized the throne for seven months. He was then ousted in a coup lead by a nobleman called Darius in 522 BCE. The new ruler went on to become Darius the Great (r. 522-486 BCE), spreading Achaemenid power to its greatest extent.
Darius built the glorious capital city of Persepolis, and also started the Greco-Persian Wars that would continue from 499 to 449 BCE. Xerxes I (r. 486-465), son of Darius, vowed to put a stop to the Greek uprisings, but even with a massive invasion fleet he was unable to overcome the Greek resistance.
Over the next 100-plus years, the Achaemenid Empire witnessed flourishing cultural accomplishments, and bloody succession struggles for the throne. The tottering Achaemenid power held up for four years under attacks from Alexander the Great of Macedon, but in 331 BCE Alexander crushed the armies of Darius III at the Battle of Gaugamela. Darius was assassinated by some of his own men; Persepolis and Susa surrendered to Alexander the following year. It was the end of the Achaemenid Empire.