Sure, I'll bite.
"What's so great about the School of Invention?" you ask? Let's break it down.
DESCRIPTION AND FLAVOR TEXT
This School claims credit for inventing all other schools of magic. They are magical inventors, as the name implies, and believe that extreme experimentation is the best way to learn. "Most wizards are scholars who have mastered their craft through careful study, rigorous practice, and endless hours of repetition," the write-up says. "(The School of Invention) wizards would rather throw spells together and see what happens." Many Invention wizards are gnomes, alchemists, or both, and are regarded as savants and/or lunatics.
Sounds like this and the Artificer are going to have a lot in common. (They won't.)
2nd LEVEL FEATURES
Tools of the Inventor: Gain proficiency with two tools of your choice. Don't fret over which ones to choose; none of the Invention class features use or require tools.
Arcanomechanical Armor: Gain proficiency with light armor, and get a suit of magic armor that only you can attune to. (It's essentially a suit of studded leather armor of resistance (force), that only weighs 8 pounds. You can transfer this benefit to any other nonmagical suit of studded leather armor over a Long Rest, but I'm honestly not sure why you would. It's pretty great right out of the tin.
Reckless Casting: you can attempt to cast a spell you don't have prepared. The mechanic is a bit clunky...you use your action, and then you choose either a cantrip or a spell slot of up to 5th level. If you choose cantrip, you roll a random cantrip and cast it as part of that action. If you choose spell slot, you roll on a random table and cast either the spell you wanted to prepare, or the spell you rolled randomly.
The random cantrips and spells are a blend of "greatest hits" spells from all spellcasting classes: flame strike, magic missile, mass cure wounds, blight, fireball, thorn whip. So more often than not, you are probably going to want the random result. It's a great way to fish for better spells, if you aren't picky about what you catch.
6th LEVEL FEATURE
Alchemical Casting: this ability has nothing to do with alchemy, potions, or even the Alchemist Tools...it's an armor buff. When you cast a spell while wearing and attuned to your suit of Arcanomechanical Armor, you can burn an extra spell slot to change the damage type of elemental spells, or cause it to deal an extra 2d10 force damage. Depending on the situation, this can have varying levels of usefulness.
10th LEVEL FEATURE
Prodigious Inspiration: as a bonus action, you can replace one spell you have prepared with another spell from your spellbook. This lets you treat your whole spell book as a list of "prepared spells," if you don't mind spending your bonus action every round. But the real benefit is out of combat, letting you re-spec all of your prepared spells.
14th LEVEL FEATURE
Controlled Chaos: When you roll a random spell (not cantrip) with your Reckless Casting feature, you can roll on the table that is one level higher than the expended spell slot. Basically you can turn a 2nd level spell slot into a 3rd level spell, so long as you aren't picky about which 3rd level spell you end up casting.
So. With all that in mind...what do you think?