NosTale comes with a main quest, that stretches across the entire playtime. It begins with Act 1, episode 1 (Act 1-1). To complete an episode in an Act, the Hero mission must also be successfully completed.
You can obtain secondary quests through Sound Flowers, that you will receive either at the end of a time-space or from defeated monsters. Secondary quests tend to contain collection or hunting quests. They are independent of the main quest and you can start five of them at the same time.
You can also accept special quests to receive Specialist Cards. For these, you have to search for the Mysterious Soulstones that can be found on general maps. These tasks are particularly challenging and time-consuming.