How did the marathon battle begin and end? Why didn’t the Spartans participate in the battle?

The battle began with a swift attack by the Greeks on the landing troops of the Persians. This ended in a battle with the defeat of the Persian troops, in the end they climbed onto ships and sailed away. The Spartans were not in the battle, since they were not interested in the fate of Athens and the war with the Persians. True, the victory in the Battle of Marathon in 490 BC caused a turning point in the war. So before that, the Greeks were mostly inferior to the Persians, but after the first major victory, the Greek poleis began to unite against a common threat.