My friend is going to host a one-shot heist campaign and I picked Arcane Trickster and the dungeon master wants us leveled up to 6. I just need re-clarification about spells. You know three cantrips, that I understand.
My question is, at level 6, how many Wizard spells can I know, and are cantrips included in the number of spells known?
I know it says we can only know 4 spells, so does that mean the 3 cantrips and then 1 first level? It says 3 spells slots for 1st level.
The Spells Known column of the Arcane Trickster Spellcasting table shows when you learn more wizard spells of 1st level or higher.
(emphasis added)
Cantrips have a spell level of 0 so they aren't included in the number of spells known.
So at 6th level you know 3 cantrips and 4 1st level spells (because you only have 1st level spell slots at that level).
In the table in PHB 98, you can see two columns for Cantrips Known and Spells Known. This means, cantrips are different from spells for the purposes of knowing them. At 6th level, you know three cantrips and four 1st-level Wizard spells.
Spells Known of 1st-Level and Higher. You know three 1st-level wizard spells of your choice, two o f which you must choose from the enchantment and illusion spells on the wizard spell list.
So two of your starting spells will be illusion or enchantment, and first level. The other can be any first level wizard spell.
Looking at the chart, you'll see at level 4 you get another spell. This spell has to be illusion or enchantment.
The chart also says you have '3' under the 'level 1' spell slots. Meaning you can cast three spells, that are level one, but only three times. These slots reset on a long rest.
So to recap...
At level 6 you will have three spells, of which are illusion and enchantment, and one of which are of any school. This makes a combined total of four. These spells are all level one. You can only cast three spells, any of them, before taking a long rest to get your slots back.
You also know three cantrips.
I hope that clears things up.
Wizards are kind of unique among spellcasters. Bards, Sorcerers and Warlocks have a set limit to the number of spells they can know, but they can cast any spell they know as long as they have spell slots available. Clerics and Druids on the other hand have access to every single spell on their spell list, but they must prepare the spells they wish to use that day after completing a long rest.
Wizards on the other hand are kind of half way between these. All of the spells you know are written down in your spellbook, and you must prepare the ones you want to use that day from those you know. You can prepare a number of spells equal to your wizard level + your int modifier. But the best part is that you can copy spells from spell scrolls or other wizards' spellbooks into yours - as long as that spell is on the wizard spell list. It's a long and expensive process, but eventually you can have access to ALL the spells on the wizard's spell list.
So at level 1, your spell book contains 6 first level spells of your choice. Assuming an int of 16 (modifier of +3) at level 1, that will give you a total of 4 spells you can prepare, out of the 6 spells you have written down in your spellbook. At level 3, you will have learnt 4 more spells (not including any additional spells you may have copied into your spellbook), and will now be able to prepare 6 spells.
One last thing, any wizard spell you have in your spellbook has the ritual tag, you can cast it as a ritual which means you don't need to have that spell prepared to cast it, and it doesn't cost you a spell slot. This process takes 10 minutes though, so you can't really cast them in combat, but as most ritual spells are for utility like identify, detect magic, leomund's magic hut, etc, this is usually not an issue.
