The Adventure of Link takes place after the original Zelda game. Ganon is dead and the Triforce of Power has been reclaimed, but Hyrule is still in a time of chaos and disorder. Some of Ganon's minions remain, waiting for his return. The only way he can return is if Link is sacrificed and his blood is sprinkled over Ganon's ashes. Link decided to stay in Hyrule to help restore it after his victory. On his sixteenth birthday, the mark of the Triforce appeared on his hand. Concerned, Link went to see Impa who became frightened when she saw the mark. She took Link to the North Castle and showed him a door that only descendants of Impa's family knew how to open. She pressed his hand against the door, and it unlocked. On the other side of the door lay Princess Zelda on an altar. Impa then went on to tell Link a legend. When the king of Hyrule died, the prince was supposed to become the king. However, he couldn't inheret the entire Triforce. He then found out from a magician that before the king died he told Zelda something about the Triforce. The prince tried to find out what it was, but she wouldn't tell him. The magician threatened to put Zelda into an eternal sleep if she didn't tell him what is was she knew. Still, Zelda said nothing. Enraged, the magician cast a sleeping spell on Zelda. The prince tried to stop him, but the magician fought him off. As Zelda fell asleep, the magician died. The prince placed Zelda on the altar behind the locked door and so that this would never be forgotten, he ordered that every female child born into the royal family be called Zelda.
After telling this to Link, Impa took six crystals and a scroll from a stand next to the altar and gave them to Link. She told him that the key to uniting the Triforce is in the scroll, but that no one could read it. Since Link had the mark on his hand, however, he could. After reading the scroll, Link found out that the three kinds of Triforce (Power, Wisdom, and Courage) must be united to bring the Triforce to full power. Two of the pieces remained, but the Triforce of Courage had been hidden in the Great Palace. To reach it, the "binding force" needed to be undone. When the six guardians are defeated and the six crystals set in the foreheads of certain statues, the "binding force" will be undone. There the Triforce of Courage would be found once the last guardian was defeated. Because Link had the crest on the back of his hand, he was destined to find the Triforce of Courage. If the entire Triforce was used, the spell on Princess Zelda could be broken. With his sword and shield in hand, Link accepted his quest.

Zelda II: The Adventure of Link plays very differently from the original. When moving around the overworld, the game takes on more of a Final Fanatasy style. However, unlike Final Fantasy's random battles, enemies can be seen in Zelda II, but they only appear when Link wanders off the road onto other terrain. Two types of enemies appear on the overworld map: strong and weak. They move quite quickly and are hard to avoid. Unlike The Legend of Zelda, Link cannot fight the enemies in the overworld. When he comes into contact with either of the two types of enemies, he is thrown into a 2D world which can be described as Mario crossed with Zelda. The game becomes a side-scroller and Link can perform abilities that he has gained throughout the game here. To escape, all you have to do is move far enough to the right or left, but there are enemies that you'll have to fight or avoid (depending on how you want to play). All of the game, except for the overworld, is played in the side-scrolling mode. Caves, towns, palaces - it's all side-scrolling.
Zelda II also features an RPG-style levelling up system. When Link defeats enemies (again, in side-scrolling mode) he gets experience points. Experience points vary from enemy to enemy. Link can also gain experience points from certain bags that are hidden throughout Hyrule. When he gets enough points Link gets a level up. At this point, the player can choose to upgrade Link's strength, health, or magic. And, like in all NES RPGs, Link can only get stronger up to a certain point. When his health, magic, and strength are maxed out (level 8), experience points mean nothing.
Also, like the original Zelda, this game is light on the side-quests. Aside from collecting Heart Containers and Magic Containers, there isn't much to do in the way of side-quests. However, this game is very heavy on magic. Link can learn a total of eight spells, each different from the rest. From a spell to gain life, to a spell that turns Link into a fairy, to the all-powerful Thunder spell, magic must be used wisely (and sometimes sparingly) to advance in this quest. The items in this game are also very non-traditional and unlike other Zelda games, items can't be used at will, only at certain points. For example, the hammer can only be used by moving up to a rock and pressing A. It can't be equipped and used to fight enemies.
Zelda II: The Adventure of Link is a Zelda game that stands apart from the rest - whether that is a good thing or a bad thing is up to the gamer to decide. From it's RPG-style levelling up system to the Mario-style side-scrolling platformer elements, this is probably the biggest departure from the traditional Zelda style a game in the series will see. Some fans may be turned off by this, but those who haven't played the game should still give it a try.