Speelbook Questions from a Noob

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I am a first time DM running new players(I am new myself) through the Twisted Halls.  One thing I am very unclear on, especially as the adventuring party has just made it level 2, are the following regarding the wizard's Spellbook...

1. How many(and of what kind) of spells(powers) can he memorize and use each day?

2. The portion of the player's handbook on a spell "vanishing" once a new one is learned is unclear to me.  Is there a table I am missing that explains just how many of each kind of spells he can learn and use daily?

Sorry for the noobie questions.  I have the Player's handbook(1), DM Guide and all of the Essentials books if you need to refer me to something specific. 

Thanks in advance for any assistance!

P.S. Sorry I didn't spell "spellbook" correctly in the thread title...how ironic!
He can memorize one spell of each choice he gets. For instance, as he is now level 2, he picks one of his level 1 daily spells and one of his level 2 utility spells to prepare each day. When he reaches level 5 and gets another daily spell, he prepares one level 1 daily, one level 5 daily, and one level 2 utility. You cannot prepare two level 5 dailies instead of one level 1 and one level 5.

On page 29 of Player's Handbook 1 is the Character Advancement Table that tells you what you get at each level. At levels 15, 19, 25, and 29 you get the choice of new daily spells, however you have to replace one of your old daily spells to take the new one. This keeps you at a grand total of 4 (8 for a wizard) daily spells known; 3 from normal class levels (6 for a wizard), and 1 from your paragon path. This actually applys for all classes; the section about the previous spell disappearing just explains that you don't keep the previous spells.

The spell vanishing also applies if you retrain one of your spells (explained on page 28 of the Players Handbook).
A Wizard gets the same standard number of the powers per day as a character of any other class. The spellbook just grants the Wizard the ability to know multiple powers and then choose different powers after each extended rest.  There are some feats paragon paths that may allowed the Wizard to know 3 spells per level instead of 2 or to memorize an additional spell each day, but those are cases of a specific rule overriding the general rule.

There's some variation depending on exactly what type of Wizard we're talking about.  The PHB Wizard (aka "Arcanist"), at level 2 will know two level 1 daily powers and two level 2 Utility powers.  At each extended rest the Wizard chooses which Daily Power and which Utility Power will be prepared for that day.
   When the Wizard reaches 5th level, he learns two more daily powers of level 5*.  After each extended rest, the wizard would prepare one level 1 daily power, one level 5 daily power, and one level 2 Utility power.
  *The wizard could take a level 1 power here instead of a level 5, but it has to be noted as such for spell prep purposes. When the wizard rests he chooses one of the two daily powers he took at level 5, whether its the level 1 power or the level 5 power, and that level 1 power cannot be taken in place of one of the daily powers he took at 1 level (without retraining to swap them) - the level at which you took the power is the important part
  There's a table available of how many spells the wizard prepares per level.  This is in addtion to Encounter powers, Cantrips and At-Will powers


The Mage from Heroes of the Fallen Lands is similar, but the Mage also gets to select Two Encounter powers everytime he would gain an Encounter attack power, and put them in the spellbook.  The mage then selects encounter powers after each extended rest in addition to daily and utility powers.  Mages also don't remove lower level spells from their spell book as they gain levels (example, at level 15, they add two more dailies, but don't have to remove the ones from 1st, 5th or 9th level), so they can prepare spells from any level after they rest as long as they don't pick two spells from the same level.

 Mages lose the implement mastery of Arcanists, and tend to do best when focused on spells of a single school, but they gain more versatility by being able to swap encounter powers and keep all the powers they gained over their career available for preparation.
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