In the PHB under The Book's Appearance the text give two examples of how a spellbook looks like a book and one example with it being just a collection of notes.
Does a Wizard's spellbook need to be a book?
Can a spellbook look or even be something else rather than just a book?
For example, could it be a series of small scroll tubes tied together like a rope ladder?
A necklace of marbles where each marble was inscribed with a single spell?
Elaborate wood carvings on a puzzle-box?
Colourful tattoos on the backs of slaves? (I'm not saying it won't be awkward when a Dragon eats pages 21 to 34 when adventuring, just asking if it would be allowed.)
Runes on the faces of convex regular icosahedron? 😉
Best Answer
No, it doesn't need to be a book.
From the "Your Spellbook" sidebar in the wizard's Spellcasting feature (PHB p. 114):
The loose collection of notes says to me that it doesn't have to be a book. I remember playing with a wizard who had a metal ring with thin sheets of metal attached as his "spellbook".
After playing for over 30 years, while the norm is the spellbook, there have been many characters that have a used different things to go along with the feel of the character. Empower the character, don't limit.
As @Rubiksmoose points out, the "Spellbook" section on Xanathar's Guide to Everything p. 58 lists some other examples of unusual spellbooks, including:
and