At 1st wizard level, you can designate a kind of item to be your arcane focus during rest by spending one rest dice.
An arcane focus is a casting implement and trusty tool used by court mages. Once a focus type is chosen, it cannot be changed, but you can swap out a focus item by designating a new focus item during rest.
The following focus item types are available:
Ring - Has two extra arcane focus points. Per +1 bonus, it grants you +1 AC. Must be a mundane ring before choosing.
Spear - The spear uses your casting modifier. When making a successful melee spell attack, you can choose to also deal weapon damage from the spear as though you hit.
Staff - Choose a level one spell of any class. The staff can be used to cast it once per rest.
Wand - You can transform a wand(or resture a burned out wand) during a rest to be your personal arcane focus item. Choose 2 cantrips. The wand can now be used to cast them at will. The cantrips consider your character level for upgrades. You can retain the wands previous spells and use the arcane focus points to cast them in place of charges.
An arcane focus has arcane focus points equal to 1/2 your lvl(rounded down, min 1.) Arcane focus points can be used to cast spells you know, by converting one focus point to 1 lvl of spell slot. All focus points are regained uppon long rest.
At 2nd wizard level, choose two upgrades:
Alchemical theory - Gain proficiency with alchemists tools or with nature. Your transmutation spell DC is increased by 1. Gain +1 bonus to checks made to identify materials and their workings. Gain a +1 bonus to checks made to persuade, interpret, or negotiate with alchemists, tinkers, and artificers.
Arbitrage - You gain a +3 bonus to checks made to create legal documents, papers, or to negotiate deals and agreements with other entities. You gain a +1 bonus to saves made vs magical rune or text effects.
Architecture and engineering - Gain proficiency with either mechanism or mechanics tools. Gain a +2 bonus on checks made to interact with golems, and mechanical hazards.
Entrepreneurship - Gain a +2 bonus to checks made to manage and run a venture or enterprise. Gain proficiency with a set of tools of choice.
Hex familiarity - Gain a +1 bonus to saves vs hexes and to AC vs hex attacks. Learn a minor hex and major hex. Gain a +1 bonus to wisdom.
Husbandry knowledge - Gain proficiency with handle animal and nature. Gain a +2 bonus to checks made to examine, identify, or determine the locations of the lairs and nests of beasts.
Knowledge of the realm - Gain proficiency with history. If already proficient, gain expertise. Gain a +2 bonus to checks made to interact with nobility, guild leaders, and establishment owners.
Medicinal arts - Gain proficiency with medicine and physicians tools. You can spend 1 rest dice to grant a creature a +1d4 bonus to a save vs a disease or blight during a rest. You gain a +1 bonus to saves vs disease.
Noetic practice - Gain proficiency with one of nature, history, arcana, or religion. Your intelligence considered 2 higher only during rest.
Oration and rhetoric - Gain a +2 bonus to checks made to address crowds, groups, or followers. Gain proficiency with 1 of persuasion, intimidation, or deception.
Religious ties - Gain proficiency with religion. You have a +2 bonus to checks made to interact with oathbearers, members of organized religions, and spiritual leaders.
Sparring practice - Gain a +1 bonus to dex and strength. Gain a +1 bonus to block checks. Gain proficiency with acrobatics or athletics.
Spycraft training - Gain proficiency with either deception or persuasion. Gain a +2 bonus on checks made to interact with criminal leaders and organizations, as well as occult group and coven members.
Theatrical arts - Gain proficiency with performance and one instrument of choice. Your enchantment spell DC is increased by 1.
Tradecraft - Gain proficiency with persuasion. You gain a +2 bonus to checks made to negotiate prices or terms.
At 2nd wizard level, you can invoke your arcane focus once per rest. When doing so, restore 1 arcane focus points to it and grant it a +1 bonus for 10 minutes.
At 3rd wizard level, you have 1 extra spell slot per every level of slot that you can cast.
At 4th wizard level, choose one upgrade from the list below:
Arcane banner - Requires spear or staff arcane focus. You can spend 2 rest dice or arcane spell points to place your arcane focus into the ground and display a banner, flag, or sign. Creatures within 20ft of the banner gain a +4 bonus to saves vs spells and effects not originating from within the banners area. The effect is lost once you move or take the arcane focus. You can use the items arcane focus points while within the banners range.
Arcane focus ward - Requires wand or staff arcane focus. You can spend 2 arcane focus points or rest dice to attempt to counter an area of effect spell or ability that deals damage or debilitates in a 10 ft radius around you. Make an arcana checks vs the effect DC. On a success, all creatures within 10 ft of you ignore the spell or ability.
Arcane spear - Requires spear arcane focus. You can spend 1 rest dice to make an attack with your focus the attack gains reach II. If it lands, you deal an extra instance of damage for everything the attack deals as force damage.
Empowered staff - Requires staff arcane focus. You can also emplace a lvl 2 spell into the staff and cast it once per long rest. The staff has +1 max arcane focus points.
Extra focus points - Your arcane focus has +2 max arcane focus points.
Extra arcane invocations - You can use invoke arcane focus an extra time once per rest.
Enchanted ring - Requires ring arcane focus. The arcane ring also provides a +2 bonus to an attribute of choice.
Greater invocation - When using invoke arcane focus, you recover 1 extra arcane focus. The duration is increased to 1 hour.
Power staff - Requires staff arcane focus. Up to once every 10 minutes, you can upcast one spell you cast by 1 level.
Reverse recall - Requires spear arcane focus. You can blink to your arcane focus.
Ring of mastery - Requires ring arcane focus. While wearing the arcane focus, your cantrips gain an extra upgrade. The upgrade can be swapped by spending 1 rest dice during a rest.
Ring of power - Requres ring arcane focus. Your arcane focus ring does not count towards your ring slot. It has +2 max arcane focus points.
Ring of protection - Requires ring arcane focus. The rings enchanted bonus also applies a +1 bonus to saves vs spells and block. The ring has a permanent +1.
Siege rip - Requires staff, wand, or spear arcane focus. You can spend 1 rest dice or arcane focus point to shatter up to as many surface tiles as your casting bonus, starting from a tile within 10 ft of you. The surface is turned to difficult terrain, earthenware or wooden structures take 2d12 force damage, weak walls or stones are shattered, and creatures standing on the tiles must make a dexterity save and take 1d8 + casting bonus force damage.
Spell-weaving - Requires ring arcane focus. Your spell focus can be used to store an extra prepared spell. Effectively, you can prepare 1 extra spell of any level you can cast. It has +1 max arcane focus points.
Staff of light - Requires staff arcane focus. You can spend 1 rest dice or arcane focus point to do the following maneuvers with your staff:
Force push - As an action, choose creatures in up to a 25 ft cone. They must make a constitution save. One a failure, they are pushed back 15ft and fall prone. On a success, they are pushed back 5ft.
Illuminate - As an action, cause arcane light to flow out of your staff and fill a 60ft area around you. All creatures within it immediately remake saves vs ongoing spell effects or curses, invisible creatures must make a wisdom save to not lose invisibility, and illusion effects are disrupted for the duration. lasts 3 turns.
Hold - As an action or reaction, cause a creature, 5ft sphere, or medium or large object in motion within 30 ft to be suspended until the start of your next turn. Negates fall damage. Can be used on an area to grant attacks passing through disadvantage.
Shield ring - Requires ring arcane focus. You can spend 1 rest dice or 1 AP while wearing your arcane focus to gain a +6 bonus to a save vs a spell or magical ability, or to a block check vs a magical attack.
Spectral assault - Requires spear arcane focus. You can spend 1 arcane focus point or 1 rest dice to make a sweeping line on a surface emit specral spears and strike at creatures within the area. Effects a number of tiles equal to your inteligence modifier + 2(min 1) and can either project the line outwards from your melee range, or parallel to you within a 15 ft radius. All creatures within the areas affected must make a dexterity save, taking a copy of your spear attack on a failure.
Spell reap - Requires spear arcane focus. When casting a cone spell or ability that requires saves from targets, you can sppend 1 rest dice or arcane focus point to make wide attack with your spear instead, making a spell attack instead. Creatures hit take the damage of your spear and are treated as failing the spell.
Staff of the magos - Requires staff arcane focus. You can copy another spell being cast within 30ft as a reaction. If the spell is higher than 2nd level, you must make an arcana check vs the spell DC. On a success, the spell is copied into the staff and can be cast once per rest.
Versatile wand - Requires wand arcane focus. You gain a +1 bonus to spell attacks made with wands. Add another cantrip to the wand, and grant all wand cantrips an extra upgrade.
Wand dueling - Requires wand arcane focus. You can attempt to dispell a directly targeted spell aimed at you while wielding your arcane focus as a reaction, by spending 1 rest dice or 1 arcane focus point to make an arcana check vs the DC of the spell. On a success, it is dispelled. On a critical success, you can redirect the spell.
Wand ennervation - Requires wand arcane focus. You can spend 1 rest dice or arcane focus points while wielding your arcane focus wand and casting a spell, or when a spell is being cast within 15 ft of you, to upcast it by 1 level.
Winged spear - Requires spear arcane focus. You can also apply spear damage on ranged spell attacks within 60 ft, as though the spear was used for the spell attack. Your spear arcane focus can be recalled to your hand as a bonus action.
At 5th and 6th level, choose another.
At 5th wizard level, gain a +2 bonus to either charisma or wisdom.
Also, choose a category of people that you gain a +2 bonus to persuasion, insight, deception, and investigation checks on:
Nobility
Merchants and traders
Craftsmen and builders
Guild, gang, and trupe leaders
Criminal elements
The underclasses and exiles
Commoners
Travelers, Sailors and explorers
At 6th wizard level, your arcane focus gains a permanent +1 bonus on top of other previous bonuses.This bonus transfers across different arcane focuses. Your arcane focus also has a +1 maximum arcane focus points. It regains 1 arcane focus point per rest.