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I'm a little stumped with this.

Example, casting a spell, 1 standard action provokes attack of opportunity. The enemy is allowed a single melee attack.

So, each time the wizard casts a spell, standard action, an enemy is allowed to basically take a free swing (melee attack) at the wizard, in hopes of interrupting the cast? When this happens, are initiatives ignored for this free single hit, allowing the enemy to go first with the 1 extra attack against the caster?

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Yes, it’s “free”

Each person can only do it once per round, but every round if a mage casts within someone’s threatened range, he provokes from that person, who gets the Attack of Opportunity. This does not require a particular action, does not require any kind of preparation, and does not affect initiative.

No, it does not allow the enemy to go first

You cannot make Attacks of Opportunity if you are flat-footed, e.g. if you have not yet acted in the combat. So in the first round (and maybe in the surprise round), the mage can cast freely around those who have not acted yet. After their first turn, they may start taking Attacks of Opportunity.

Combat Reflexes changes these

The Combat Reflexes feat allows a number of Attacks of Opportunity equal to one’s Dex mod, and further allows Attacks of Opportunity while flat-footed.

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    \$\begingroup\$ The caster can also cast defensively in order to deny the attacker the attack of opportunity, this does give a chance of losing the spell instead however. \$\endgroup\$
    – Rob
    Jun 13, 2013 at 7:51
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    \$\begingroup\$ This is a great answer, but I'd consider adding a section for concentration checks and casting defensively. You either have a concentration check based on taking damage during spellcasting or one based on casting defensively. \$\endgroup\$ Jun 13, 2013 at 15:22
  • \$\begingroup\$ @JacobProffitt This is tagged Pathfinder, so no Concentration. I figured that Rob's comment handled Casting Defensively well. \$\endgroup\$
    – KRyan
    Jun 15, 2013 at 10:48
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    \$\begingroup\$ @KRyan You might want to review the rules on that... d20pfsrd.com/magic#TOC-Concentration \$\endgroup\$ Jun 15, 2013 at 18:44
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    \$\begingroup\$ @KRyan Pathfinder didn't drop concentration mechanics outright, they just took it out of being a skill and made it a level check instead. \$\endgroup\$ Sep 16, 2013 at 23:31
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It's a little better and a little worse than you doubt.

First of all, if you cast a spell without casting defensively, you get one attack of opportunity from each single enemy that has you in its threat range, unless they've already done an AoO in that round.

This means several different things.

One AoO per enemy, but only if he's near

First of all, anyone willing to punish you for trying to cast needs to have you in melee range and to wield a weapon (or have the improved unarmed strike feat).
Several enemies could satisfy these conditions and each one gets the possibility to use his once-per-turn extra attack on you.

This means you can usually step back to avoid AoOs. Unless the movement also nets you some AoOs (which you can avoid by taking a 5ft step only or by making tumble checks.
While this is a basic and awesome tactic, there are situations where you don't want to step back, like if the spell you need to cast is a touch range one.

The enemy goes first

Second, yes, the attack happens before you complete your action. It means the attack can disrupt your casting by damaging you while you're casting a spell, just like if the enemy prepared against you casting a spell but is a free action (and thus a gain in the action economy).
This does not mean the enemy goes first in the initiative count. Unless he has the Combat Reflexes feat a character can't make AoOs while flat-footed.
This means you, as a spellcaster, should not normally worry about AoOs if you win initiative. But you're not usually in the threat range of any enemy when that happens, right?

One AoO only between your turn and the next one

Third, they need to choose if they want to make the AoO on you or on someone else, should the opportunity arise. You could trick them into attacking you to let the barbarian run amongst them with no risk... or the opposite (provided the second one of you acts before the enemy turn, when he recharges his AoOs).
It's worth noting that the Combat Reflexes feat allows a character more AoOs between their turns and this can nullify such a ruse.

The usual solution

There's another way to avoid AoO for spellcasting and it's called casting defensively. You just declare you're casting defensively and you don't provoke AoOs anymore. You need to pass a concentration check to successfully cast the spell. The DC is manageable and your modifiers should be high so this is the safe and intended way to do it.

Bonus info: if you need to cast a touch spell remember you can get your move action between the casting and the delivery. This means you cast it outside melee threat range, then move in.

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    \$\begingroup\$ You might want to tweak your wording -- you keep track of the number of AoO you've made since your last turn, not per round. For a new player this distinction is important to make. \$\endgroup\$
    – starwed
    Jun 16, 2013 at 19:01
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    \$\begingroup\$ Good answer, though in Pathfinder (and this question is specifically tagged Pathfinder), concentration is no longer a skill and thus doesn't have "ranks". A concentration check is simply your caster level plus the modifier for the relevant caster ability (Int, Wis, or Cha). Some traits or feats may add to it, but still no ranks. \$\endgroup\$ Jun 17, 2013 at 15:33
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What is worse, is many spell that are not Touch Attacks... would be considered as Range Attack. ( Or Touch attack spell, effected by the "Reach mentmagicfeat", are Range Touch Attack

All Range attack spell, also create another AoO, see page 186 CrB.

Thereby, generating two chance for AoO, for casting one spell (( all though most character could only make use of one, unless they have Combat Reflexe feat)).

..............

side note: many people forget that Spontaneously cast spell take twice as long to cast as normal. Combine this with the 1 round cast time of summon spells, and most Spontaneously cast summon nature ally druid spell will take effect just before the druid turn in round 3, at which point they can then take action or cast another spell in round 3.

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  • \$\begingroup\$ Spontaneous metamagic casting doesn't double the cast time, it ups standard cast times to full round actions (which is not a 1 round cast time, so it still goes off on your turn) and anything longer only takes an extra full round. So a summon monster spell would normally go off at the beginning of your second turn, but you would have to spend an extra full round action causing it to go off at the end of the second turn. If it added a 1 round action then it would go off right before the third round. \$\endgroup\$
    – JStephen
    Jun 14, 2015 at 0:42

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