*Updated for U9*
Since this is a common question asked by new Wizards, I compiled this list to help out, and will try to keep it updated, mostly for easy viewing from the in-game web-browser.
This is a list of arcane spells which will have to be learned from a Wizard trainer, found on scrolls in loot, or purchased from another player. You will not be able to purchase these scrolls from an NPC for scribing into your spellbook.
•Level I:•
Acid Spray
Sonic Blast
•Level II:•
Electric Loop
Gust of Wind
Lesser Death Aura
Scorch
Snowball Swarm
•Level III:•
Acid Blast
Chain Missiles
Frost Lance
•Level IV:•
Death Aura
Dimension Door
Negative Energy Burst
Solid Fog
Symbol of Flame
Wall of Fire
•Level V:•
Cloudkill
Cyclonic Blast
Eladar's Electric Surge
Niac's Biting Cold
Repair Light Damage, Mass
Symbol of Pain
•Level VI:•
Acid Fog
Create Undead
Necrotic Ray
Repair Moderate Damage, Mass
Symbol of Fear
Symbol of Persuasion
•Level VII:•
Delayed Blast Fireball
Otto's Sphere of Dancing
Prismatic Spray
Protection from Elements, Mass
Repair Serious Damage, Mass
Symbol of Weakness
•Level VIII:•
Greater Shout
Horrid Wilting
Incendiary Cloud
Mass Charm Monster
Otto's Irresistible Dance
Polar Ray
Power Word: Stun
Repair Critical Damage, Mass
Summon Monster VIII
Sunburst
Symbol of Death
Trap the Soul
•Level IX:•
Dominate Monster
Energy Drain
Hold Monster, Mass
Meteor Swarm
Mordenkainen's Disjunction
Power Word: Kill
Summon Monster IX
Wail of The Banshee
In addition, the following two scrolls are available at the NPC merchant in The Portable Hole, however, you won't be able to go there and buy them until you reach level 9, and can Teleport to that location.*
Master's Touch
Merfolk's Blessing
*Note: You can always buy a scroll of Teleport before you reach level 9, and attempt to use it to get to The Portable Hole, though it might misfire and require use of more than one scroll. In addition, you could ask a friendly Wizard or Sorcerer for a Greater Teleport, and hitch a ride. (Thanks shagath & Rusty_Can!)
Is this list complete? I hope so. If I missed a spell, or there's one on my list that shouldn't be, please reply and let me know.