The wizard group encompasses all arcane spellcaster classes: the mage, illusionist, and the other seven specialist wizards. Each of these specialist classes is an expert in a corresponding school of magic. Thus, the conjurer specializes in Conjuration/Summoning spells; the transmuter specializes in Alteration magic; and so on. A notable quirk of the nine schools is that one - Lesser Divination - does not have a specialist class (although its advanced form, Greater Divination, does have one in the Diviner class). The spells of this school, enumerated in the rules as all Divination spells of 4th level or below, are essential to the work of any and every wizard, and so can be learned and cast by any wizard class. The 1st-level spell cantrip is also available to all wizards, as it is present in every school.
In addition to their favored school, each specialist class has one or more opposition schools, from which they can never, ever learn or cast spells under any circumstances (barring divine intervention or, at the DM's discretion, a wish spell). Under the standard rules given in the PHB, specialists gain a bonus to learn spells from their favored school (as well as an extra spell slot and a saving throw bonus for such), and a penalty to learn spells from other schools which are not their opposition school.
|Diagram illustrating the schools of magic.|
From the 2nd Edition Player's Handbook, 1995.
The mage class is not available to player characters. Arcane magic is an esoteric discipline that requires a naturally strong mind and years of rigorous training; the notion of anyone with average intellect and a cheap spellbook being able to learn magic of any and every school is ridiculous.
All wizards must be specialists. The specialist classes available to a character (depending on ability scores and race) are the same as those given in the PHB; the level limits for demihuman specialists are the same as the ones for mages given in the DMG. Note that to become a specialist, a character must not only meet the ability score requirements for their race (if demihuman) and those for their chosen specialist class, but also have the 9 (preferably much higher) Intelligence required of a mage in the standard rules. Thus, a player hoping to play an elf enchanter would need at least 6 Dex, 7 Con, 9 Int, and 16 Cha, and would have a maximum level of 15 (unless the optional Slow Advancement rules are used). The total unlikelihood of getting all of these in order is one reason why I usually use Method III to roll up ability scores, i.e., 3d6 arranged to taste.
Per the PHB, specialist demihumans cannot multi-class, with the sole exception of gnome illusionists. Specialist humans, however, can dual-class at the DM's discretion; normal dual-classing rules still apply with regard to class groups.
Specialists can learn and cast only spells from their favored school, or from Lesser Divination, and no others. They can, however, use magic items (including level-appropriate scrolls) from other schools without penalty, except for those which duplicate spells from their opposition school(s).
If 0-level spells (cantrips) are used as they appear in AD&D 1st Edition (Unearthed Arcana and issues 59-61 of Dragon), the specialist is still limited by the school in which the cantrip is listed. For those schools which have no cantrips (notably Necromancy), the players and DM should cooperate to create new ones, without necessitating spell research in this instance. Note that cantrips of the Divination school will be available for use by all specialist wizards.