There are no regular "quests" in Mortal Online. There are however a lot of events, special places, artefacts, and rare creatures and beings in the world waiting to be discovered, used, protected or killed. Exploring the (map-less) world and finding the clues to these quests, puzzles or enigmas can often be made solo if you are prepared to take the risks. Nothing of this is really solo-play, as eventually you will have to sell your masterpieces to other players to make money, or you will have to agree with another player to transport his or her goods someplace. Or you may have trained a skill to perfection and written some skill books that you need to sell to other players to get money. But vendors will be giving players task to deliver resources if the vendor is actually missing the item.
There will be very big quests in the form of riddles and chains-of-events spread about in the world that will often involve several players or guilds, and from time to time affect the development of the world. These quests will start slowly even from day one, and SV has some deep events planned for the players - where their actions will get reflected back upon the world and the rest of the future players. They have even presented clues for some of these events before the game starts.