Part 3 of the Player’s Handbook is The Rules of Magic. The chapter opens with some text about what a spell is, known and prepared spells (some casters have a limited number of spells known- bards and sorcerers for example, others prepare spells), spell slots, casting spells at a higher level, cantrips, and rituals. Rituals are spells that can be cast as normal, or can be cast +10 minutes casting time and do not expend a spell slot when cast as a ritual.
The chapter goes on to discuss casting time, bonus actions (which are essentially swift actions, a term that has no explanation), reactions, and longer casting times. Range, targets, areas of effect, saves, attack rolls, combining effects, the schools of magic, duration, and components (material components make a return, though if you have a component pouch or focus you can ignore, unless the material component has a cost indicated or if the material component is consumed). And finally, a short bit differentiating arcane and divine magic.
And onto the spells. Spell lists organized by class and level. Even though wizards specialize in schools, there is no list of spells by school, so a character will have to have the researcher background to comb through all the spells (78 pages worth). Then the list of spells themselves, with descriptions. Of note, the descriptions do not say which class has access to them, and also the level of a spell doesn’t vary, so a Cone of Cold is a fifth level spell, no matter who casts it. Some editions have differed, in that a Bard might cast a spell as a 4th level spell, while a wizard gains access to it at 3rd. Summon Monster seems to have gone the way of the dodo.
A player playing a spell-caster will need to have a copy of the PHB (and whatever books that are released that have spells in them) and will have to flip through pages during the game, or come up with some sort of note taking (index cards with spells on them?).
Overall, it seems very much like a 3.x spell list, with less functionality from a user interface standpoint, and lots of room for interpretation, having to look up spells in the middle of a game.
Player: “I cast XXX”
DM: “What does XXX do?” (opening book).
Player and DM discuss, DM makes a ruling if necessary.
Not my preferred style of play.