Alchemist
The physical world is full of wondrous power and capability, and alchemy is little more than the art of harnessing this power for one's own use. Far removed from the magi of old, wielding their sorcerous power that sought to destroy the natural order of things, the alchemist uses his knowledge and will to unlock the potential that is already there.
Modifications to the Wizard Class
Proficiencies
Alchemists receive all the proficiencies a normal wizard would receive, with the following additions.
Armor: Light Armor
Weapons: One simple weapon of your choice
Tools: Alchemist's tools
Spellcasting
Materials-Based Casting
Magical spells cast by an alchemist have no verbal or somatic component, although all spells of level 1 or higher have a material component in the form of residuum prepared beforehand. If the spell would normally require a material component with a listed cost, that item must be a part of the alchemist's toolkit if the spell does not consume the component. If the spell would normally consume its material component, it must be ground into residuum during the spell's preparation.
Preparing and Casting Spells
During a long rest, you prepare the list of wizard spells that are available for you to cast. To do this is a slightly more complicated and restrictive process than that employed by other wizards. Firstly, you select a number of unique spells from your spellbook no higher than your wizard level + your Intelligence modifier (minimum of one spell). Secondly, you assign each spell slot of first level or above to one of the spells on the list chosen before. When the spell is cast and its assigned slot used, it may not be cast again unless it is assigned to another spell slot.
Example - Elias Radenos is preparing spells during his long rest. He is a third level wizard with a 14 Intelligence, and so he can prepare at most 5 unique spells. He chooses the following list: Burning Hands, Feather Fall, Mage Armor, Sleep, and Hold Person. As a third level wizard, he has four first-level slots and two second-level. He chose to prepare Burning Hands, Feather Fall, Mage Armor, and Sleep as first-level spells, and Hold Person and Burning Hands as second-level spells.
Overpreparation
When alchemists prepare spells to cast, it is possible to prepare more spell slots worth of spells than they would normally be able to cast, although the toxicity of the Barouti Stone required to hold the magical matrix intact is a limiting factor. An alchemist may choose to prepare the casting of additional spells where the combined total of spell levels is equal or less than the alchemist's wizard level.
Casting these spells risks the alchemist undergoing Barouti poisoning, the effects of which can be negated with a Constitution save with DC equal to 10 + the total level of spells cast in addition to their normal spell slots.
Example - Elias knows that there may be more opposition than he had anticipated, and so prepares an additional Mage Armor (first level) and Hold Person (second level) spell, a total of three spell levels, equal to his three levels in the wizard class. Over the course of the day, he casts his entire regularly-allotted spell casts and needs to cast an additional Hold Person spell. Downing his extra Hold Person potion, he must make a Constitution (DC:12) saving throw. When escaping, he casts his remaining Mage Armor spell, and must again make a Constitution saving throw, this time with a DC of 13 (10 + 2 from Hold Person + 1 from Mage Armor).
The Alchemist is modification of the Wizard class described in the Player's Handbook on page 112, adapted to allow the character to study the Arcane in a manner tolerated in Eudokonia. A player choosing to play an alchemist makes the decision when gaining their first level in the wizard class. As the Alchemist is a modification, not a subclass, the character may still choose an Arcane Tradition subclass at second level.
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