They're spontaneous casters.
They only learn spells by leveling.
A summoner’s selection of spells is extremely limited. A summoner begins play knowing four 0-level spells and two 1st-level spells of the summoner’s choice. At each new summoner level, he gains one or more new spells as indicated on Table: Summoner Spells Known. (Unlike spells per day, the number of spells a summoner knows is not affected by his Charisma score. The numbers on Table: Summoner Spells Known are fixed.)
Expanded Arcana feat(s); some races have an option to pick up additional lower level known spells.
These items give you the option to learn more spells. Pick up some of these if you don't want to blow a feat.
Ring of Spell Knowledge
Aura moderate or strong (no school); CL 7th
Slot ring; Price 1,500 gp (Type I), 6,000 gp (Type II), 13,500 gp (Type III), 24,000 gp (Type IV); Weight —
Description
This ring comes in four types: ring of spell knowledge I, ring of spell knowledge II, ring of spell knowledge III, and ring of spell knowledge IV. All of them are useful only to spontaneous arcane spellcasters.
Through study, the wearer can gain the knowledge of a single spell in addition to those allotted by her class and level. A ring of spell knowledge I can hold 1st-level spells only, a ring of spell knowledge II 1st- or 2nd-level spells, a ring of spell knowledge III spells of 3rd level or lower, and a ring of spell knowledge IV up to 4th-level spells.
A ring of spell knowledge is only a storage space; the wearer must still encounter a written, active, or cast version of the spell and succeed at a DC 20 Spellcraft check to teach the spell to the ring. Thereafter, the arcane spellcaster may cast the spell as though she knew the spell and it appeared on her class’ spell list.
Arcane spells that do not appear on the wearer’s class list are treated as one level higher for all purposes (storage and casting).
Construction Requirements
Forge Ring, creator must be able to cast spells of the spell level to be granted; Cost 750 gp (Type I), 3,000 gp (Type II), 6,750 (Type III), 12,000 gp (Type IV).
Page of Spell Knowledge
Aura strong transmutation; CL 17th; Weight —
Slot none; Price 1,000 gp (1st), 4,000 gp (2nd), 9,000 gp (3rd), 16,000 gp (4th), 25,000 gp (5th), 36,000 gp (6th), 49,000 gp (7th), 64,000 gp (8th), 81,000 gp (9th)
DESCRIPTION
This page is covered in densely-worded arcane or divine magical runes. It contains the knowledge of a single arcane or divine spell (chosen by the creator when the item is crafted). If the bearer is a spontaneous spellcaster and has that spell on her class spell list, she may use her spell slots to cast that spell as if it were one of her spells known. A page of spell knowledge is priced based on the spell's cleric or sorcerer/wizard spell level, unless the spell doesn't appear on either of those spell lists, in which case it is based on the highest spell level as it appears on any other spell list. For example, a spell that is on the 4th-level inquisitor list and the 2nd-level paladin list is priced as a 4th-level spell.
CONSTRUCTION REQUIREMENTS
Craft Wondrous Item, creator must be able to cast the spell contained in the page ; Cost 500 gp (1st), 2,000 gp (2nd), 4,500 gp (3rd), 8,000 gp (4th), 12,500 gp (5th), 18,000 gp (6th), 24,000 gp (7th), 32,000 gp (8th), 40,500 gp (9th)