As a student of arcane magic, you have learned to cast spells.
Cantrips. You know three Mage cantrips of your choice. Whenever you finish a Long Rest, you can replace one of your cantrips from this feature with another Mage cantrip of your choice.
When you reach Mage levels 4 and 10, you learn another Mage cantrip of your choice, as shown in the Cantrips column of the Mage Features table.
Spellbook. Your magical apprenticeship culminated in the creation of a unique book: your spellbook. It is a Tiny object that weighs 3 pounds, contains 100 pages, and can be read only by you or someone casting Identify. You determine the book’s appearance and materials, such as a gilt-edged tome or a collection of vellum bound with twine.
The book contains the level 1+ spells you know. It starts with six level 1 Mage spells of your choice.
Whenever you gain a Mage level after 1, add two Mage spells of your choice to your spellbook. Each of these spells must be of a level for which you have spell slots, as shown in the Mage Features table. The spells are the culmination of arcane research you do regularly.
Spell Slots. The Mage Features table shows how many spell slots you have to cast your level 1+ spells. You regain all expended slots when you finish a Long Rest.
Prepared Spells of Level 1+. You prepare the list of level 1+ spells that are available for you to cast with this feature. To do so, choose four spells from your spellbook. The chosen spells must be of a level for which you have spell slots.
The number of spells on your list increases as you gain Mage levels, as shown in the Prepared Spells column of the Mage Features table. Whenever that number increases, choose additional Mage spells until the number of spells on your list matches the number in the table. The chosen spells must be of a level for which you have spell slots. For example, if you’re a level 3 Mage, your list of prepared spells can include six spells of levels 1 and 2 in any combination, chosen from your spellbook.
If another Mage feature gives you spells that you always have prepared, those spells don’t count against the number of spells you can prepare with this feature, but those spells otherwise count as Mage spells for you.
Changing Your Prepared Spells. Whenever you finish a Long Rest, you can change your list of prepared spells, replacing any of the spells there with spells from your spellbook.
Spellcasting Ability. Intelligence is your spellcasting ability for your Mage spells.
Spellcasting Focus. You can use an Arcane Focus or your spellbook as a Spellcasting Focus for your Mage spells.
Expanding and Replacing a Spellbook
The spells you add to your spellbook as you gain levels reflect your ongoing magical research, but you might find other spells during your adventures that you can add to the book. You could discover a Mage spell on a Spell Scroll, for example, and then copy it into your spellbook.
Copying a Spell into the Book. When you find a level 1+ Mage spell, you can copy it into your spellbook if it’s of a level you can prepare and if you have time to copy it. For each level of the spell, the transcription takes 2 hours and costs 50 GP. Afterward you can prepare the spell like the other spells in your spellbook.
Copying the Book. You can copy a spell from your spellbook into another book. This is like copying a new spell into your spellbook but faster, since you already know how to cast the spell. You need spend only 1 hour and 10 GP for each level of the copied spell.
If you lose your spellbook, you can use the same procedure to transcribe the Mage spells that you have prepared into a new spellbook. Filling out the remainder of the new book requires you to find new spells to do so. For this reason, many mages keep a backup spellbook.