Jace, Meister der Erinnerung

If Jace’s third ability causes a player to draw more cards than are left in their library, that player loses the game as a state-based action. If this ability causes all players to do this, the game is a draw.

If you activate Jace’s first ability, and the player is an illegal target when the ability tries to resolve, it won’t resolve and none of its effects will happen. You won’t draw a card.

If you target yourself with Jace’s first ability, you’ll draw a card first, then put the top card of your library into your graveyard.