Alexandria was founded in 332 B.C. by Alexander the Great, the king of Macedonia (in nowadays Greece), during his conquest of Persia. During his short life he built the biggest empire of the Ancient world, spanning from Greece to India, and he is considered one of the most powerful and influential leaders of that time.
Alexander the Great was born in Macedonia in 356 B.C. as the son to King Philip II, who was a renowned military strategist with ambitions to conquer Persia. The king had Aristotle tutor his son in literature, science, medicine and philosophy, encouraging Alexander’s interest in these topics. He was left in charge of Macedonia at 16, when King Philip went to war, and became king at the age of 20 after his father’s assassination in 336 B.C.
After securing his place as king and crushing rebellions in northern Greece, Alexander left Macedonia to continue the conquest his father started. His biggest opponent was the Persian king Darius III, whose Persian armies was defeated multiple times by the smaller but more experienced and motivated army of Alexander. Alexander is said to have been a charismatic and ruthless leader, a power hungry strategist, with loyal men willing to follow him across the world.
After multiple battles and conquests of countries surrounding the eastern Mediterranean coast, Alexander entered Egypt in November 332 B.C. The Persian satrap, a provincial governor, Mazaces didn’t fight the Macedonian army and Alexander was welcomed into Egypt by its people, even crowned with the traditional crown of the pharaohs. He spent the winter in Egypt, employing Egyptian governors while keeping its army under a Macedonian command. Alexandria was founded on an already existing small town, but the much greater city was it laid out by Deinocrates, a Rhodian architect. When Alexander left Egypt in 331 B.C. he returned to Tyre in Syria, appointed a Macedonian satrap and thus stabilized his control over the entire eastern coast of the Mediterranean.
Alexander continued his conquest by going into Mesopotamia and then towards Babylon. After a bloodied battle at Gaugamela in October 331 B.C., with heavy losses on both sides, Darius fled and was assassinated by his own troops. His suspected assassinator Bessus claimed the throne. It is said that Alexander gave Darius a royal burial after finding his body, and he appointed himself king of Persia but needed to get rid of Bessus to tighten his control. Bessus was handed over to the Macedonians by his own army after a hard pursuit and is said to have been mutilated and executed by a good friend of Alexander.
Alexander was not all popular, and the Persian people were not happy when Alexander adapted some of their customs to gain their liking. But he managed to introduce Greek culture, which would prevail after his death. He did encounter resistance while trying to conquer the Persian region Sogdia, but was never defeated in battle and managed to take control of Sogdia before continuing to India. In the battle by the Hydaspes River in 326 B.C., Alexander encountered King Porus of Paurava. The Indian king’s army wasn’t as experienced as Alexander’s, but it did have elephants and thus the battle was fierce, said to have happened during a raging thunderstorm. In the end, Alexander won, but he lost his war horse during the battle, a horse he had tamed himself at the age of 12 and had brought with him all the way from Greece.
While Alexander wanted to conquer all of India, his soldiers were tired and he had to return with his army to Persia. There, in order to unite Macedonians and Persians, Alexander organized a mass wedding between Persian princesses and his officers in 324 B.C., but this was not liked by many. In fact, many of his men mutinied. Alexander then replaced Macedonian officers with Persians, and his army backed down, going through with the wedding.
While he was planning on conquering Arabia, Alexander the Great died in 323 B.C. aged 32. Some historians think it was due to malaria or some other illness, others to poisoning, and the truth is likely to never be revealed. Alexander had never appointed a successor, so his empire soon shattered due to inside fighting over power.
During his short life, Alexander the Great had become the head of an enormous empire, introducing Greek culture across the world and many of the places he conquered and founded are still considered important cultural centres. He changed the word to the extent that a new historical epoch was introduced: the Hellenistic period.

Sources:
https://www.history.com/topics/ancient-history/alexander-the-great
https://www.britannica.com/biography/Alexander-the-Great#ref59257