The Summoner is one of the endgame jobs of Final Fantasy III. It is the first 'true' incarnation of the recurring Summoner job in the series.
Like the Evoker, the Summoner specifically uses summon spells, of which there is one for each tier rather than enough to fill all three slots. However, while the Evoker has a white or black magic spell chosen at random for each summon, the Summoner exclusively uses the High summon attacks - which are almost always attacks that target the entire enemy field.
It's hard not to see the Summoner as an improved version of the Evoker. While it loses out on the utility offered by some of the white magic effects, it operates consistently. It has a single job, but it does that job well.
In the 3D remake, the biggest element affecting the Summoner is actually not tied to the Summoner itself: Rather, the Sage was nerfed to only use the Evoker spells rather than the High Summon spells. This leaves the Summoner as the sole source of High Summon attacks.
The Summon ability allows the Summoner to call upon summoned beasts to perform an attack. Unlike the Evoker, every attack that the Summoner performs will an attack. The Summoner's MP is otherwise identical to the Evoker.
Summons in tiers 2-5 (i.e. All of the purchasable summons) do the same amount of damage and have the same amount of casts, meaning that what to use when depends heavily on the which is more effective against the enemy. As Catastro results in Zantetsuken, an instant-kill attack, tiers 7 & 8 should be reserved for bosses. Escape, the tier 1 spell is singled out by the guide as never worth using: Even with the most optimal stats, Chocobo Kick does so little damage that the Summoner is better off using elemental weapon spells than using Escape.
Additionally, the Summoner has no supportive abilities unlike the Evoker. Devouts/White Mages are good for heavy support while Sages can also provide some offense. Physical damage dealers are also recommended. The guide also brings up the possibility of using two Sages, a Summoner and a Magus for an aggressive, although it also notes that such a strategy will require a surplus of elixers.