Is it possible for a wizard to change the spells in her spellbook?

Question

Wizards choose new spells to add to their spellbooks at level-up; however, through the course of play a wizard might find that one of the spells she learned is not very useful, and want to exchange the spell in the spellbook for another spell. This is to say: an existing spell in the spellbook is removed, and a previously-unknown spell is added in its place. Is this possible in D&D Fifth Edition?

Good Answers Include

1. A yes-or-no answer to the question based on citation from D&D 5E rulebooks. Twitter errata/clarifications or similar statements from the game's designers may also be cited as sufficient justification.
2. Any limitations that exist on changing spells, such as "the new spell must be the same or lower level" or "characters can only swap out a spell learned at last level up."

Answer 1

Yes, but not in the way you're thinking, and not without working for it. In the way you're thinking of it—being able to learn a new spell at the low, low cost of just giving up a known spell, no, you can't replace a spell that way.

This is because there is no mechanical resource spent to learn a spell except time and monetary expenses. There isn't a "slot" that you can empty and refill with another spell. You can know about as many spells as you can find and record in your spellbook—your spells known aren't in your head, they exist only as pages in your own notation in your spellbook. If you do forget a spell, the only effect is that you now know one fewer spell—you don't spontaneously know a replacement.

The only way to get new spells is the two freebies at level-up, and by discovering them as "treasure" during play. Further, the level-up freebies are only free to learn, and once learned it's on he wizard's head to make sure she doesn't lose the benefit of those free spells because they won't be replaced if they're lost.

The only way to forget a spell ("Your Spellbook", D&D Basic Rules v0.1, p. 32) is by losing your record of it in your spellbook when you don't have it prepared, and there are no provisions in the rules for easily replacing lost spells with different ones. In fact, you don't get any of them back for free—all your spells known have to be recreated through time, labour, and money by transcribing the few you had prepared when the spellbook was lost, and there is no way except rediscovery to replace spells that she didn't have prepared that day.

So yes, if burning your spellbook and then adventuring to find new spells counts as "changing the spells in the spellbook." But I'm fairly certain that trivially-true "yes" isn't what you're looking for, and the practical answer is no.

Answer 2

No, but there is an alternative.
You can't forget a spell and have it be replaced with a new spell in your spellbook. You can erase,burn, or rip a spell from your spell book if you like however, and will have to spend time, effort and coin to fill that space. (Spell books only have 100 pages.) (Basic Rules v0.1, page 49.)

There are two ways besides gaining levels to add spells to your spellbook. One is by adventuring, and finding old scrolls.

You might find other spells during your adventures. You could discover a spell recorded on a scroll in an evil wizard’s chest, for example, or in a dusty tome in an ancient library.

Adding these scrolls to your spellbook costs 50 gp and 2 hours per level of the spell. (You can also copy spells you already know for 10gp and 1 hour per level.)
(Basic Rules v0.1, page 32.)

Another method which is alluded to but not spelled out is by using the downtime system after discussing it with your DM. Downtime works in days, and you must spend at least 8 hours a day working on what you are trying to do. In this case, you'll be visiting a school of wizardry or a university, or an old magic shop, or meeting with an old wise wizard as a mentor.

While learning new skills, languages, and tools are explicitly mentioned as things you can do during downtime, learning new spells is not, therefore it currently falls under this paragraph:

Downtime activities other than the ones presented below are possible. If you want your character to spend his or her downtime performing an activity not covered here, discuss it with your DM.
(Basic Rules v.01, page 68)