Magic use can be one of the most versatile and rewarding parts of any character, but the rules for magic use can be a bit complicated for newer players. To fully understand how magic functions, see Spellcasting Basics section of the Core Rules, but here is a brief overview to get you started.
There are a number of different types of magic users, though they all share a common feature--spells. Magic users learn and cast spells in different ways. Some are gifted them from their deities; some intuitively know them; others imbibe them in arcane liquids. But all casters can be divided into three main types: Intuitive Casters, Divine Casters, and Scholarly Casters.
Intuitive casters automatically know a certain set of spells and so they don't have to prepare their magic each day. When you first create an intuitive caster, you know two first-level spells. These starter spells can be any on the list of 1st level spells available to your class. Later, when you level up, you will gain more.
Divine casters prepare spells every day at a set time. During preparation, you may select any spell from the list of spells available to you. This gives divine casters wide flexibility in their use of magic. You should try to anticipate your needs for the coming day and select spells that you think might work best. As a divine caster, the number of spells you can prepare each day = your level + your wisdom bonus.
Like divine casters, scholarly casters prepare spells each day, usually in the morning after a long rest. While divine casters can prepare any spell on their class list, scholarly casters (except witches) can only prepare spells that they have learned and recorded. For wizards and magi, these learned spells are recorded in a spellbook. Alchemists record these spells in a formulae book. Witch spells are stored in their familiars.
When you begin at level 1, your spellbook/formulae book/familiar begins with three spells of your choice that you already know. As you encounter more spells in the world, you may learn these and add them to your book. There is no limit to the number of spells you can eventually learn.
Like divine casters, you prepare spells each day from your book/familiar. The number of spells you can prepare is equal to your level + your intelligence bonus. Note: alchemist extracts are slightly different than other scholarly casters, so you should read the Alchemist class description for details on preparing extracts.
All spellcasters have a set number of spell slots available to them each day. In order to cast a spell, you must use a spell slot. You cannot cast without a spell slot, so when you run out, you must wait until you get them back (usually after your daily spell preparation).
All spells have a base level between 1 and 9 (we'll talk about 0-level spells in a second). First-level spells are generally weaker, and ninth level spells are stronger. To cast a spell, you need an available slot equal to the base level of the spell (2nd level spells require a 2nd level slot), but you can also power up a spell by casting it at a higher slot. Some first level spells, for instance, do more damage if you cast them in a 3rd level slot. Sometimes you can unlock different effects by casting spells at higher levels, too. Cloud, for instance, can create an obscuring mist when cast at 1st level, but you can turn that mist into a solid fog or deadly cloud when you cast it using higher level spell slots.
When you start, you begin with a handful of 1st level slots. You acquire more slots as you advance, allowing you to cast more spells at higher levels.
A handful of magic is so basic that you don't need spell slots to cast it. These are called cantrips. You start with 3 cantrips of your choice. Every five levels (5th, 10th, 15th, and 20th), you gain another cantrip.
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