Spell Hunter
You are an archivist of knowledge. But unlike those stodgy librarians that obtain knowledge and then let it rot away in their libraries, untouched, you put that knowledge to use to further glean the secrets of the arcane. You wish to know and understand the intricacies of every spell. This thirst for knowledge leads you to forgotten tombs and old ruins, but you endure. For the sake of the knowledge within.
Learned Caster
Starting at 2nd level, you have experimented with enough spells to cast them more economically. Whenever you cast a spell with a material component with a cost, it only costs you half the cost to cast.
Cantrip Mastery
Starting at 2nd level, you have learning new cantrips comes extremely easy to you. You gain a Wizard cantrip at 2nd level. You gain an extra Wizard cantrip at 7th, 13th and 17th levels.
Tiered Spellcasting
Starting at 6th level, you have learned to push more power into your spells. When you cast a spell using a spell slot higher than the spell level, the spell is considered an extra level higher when cast.
You must be able to cast spells of the final spell level to be able to use this feature.
Arcane Memory
Starting at 10th level, you know enough about magic to have to ability to cast almost any spell. As a reaction, choose a spell that you have seen cast and have a spell slot high enough to cast yourself. You can cast that spell using a Wizard spell slot and it counts as a Wizard spell for you. You lose the spell when you finish a long rest.
Secrets Unfurled
Starting at 14th level, even the spells that are mysterious to other Wizards become easy for you to scribe. You can scribe a number of non-Wizard spells into your spellbook equal to your Intelligence modifier.
Art Credits
Sea Gate Oracle by Daniel Ljunggren