In Lost Mine of Phandelver, the party comes across (and presumably defeats) multiple mages. These are not specifically described as Wizards, but their spellcasting is Intelligence-based, and they know spells from the Wizard spell list, so it sounds to me like they are Wizards. (If it quacks like a duck…)
Wizards, in D&D5e, use spellbooks. (See the "Spellbook" sub-section in the description of the Wizard class, p. 114 in the PHB.)
However, the Lost Mine of Phandelver material nowhere mentions the mages' spellbooks.
Should my party be able to loot spellbooks? Or are these BBEGs actually non-spellbook-carrying casters? Or am I overlooking something?
Best Answer
Jeremy Crawford unofficially addresses this specific issue regarding Lost Mine of Phandelver in a pair of tweets from January 2017:
The section on equipment that Crawford mentions states:
In this case, virtually all the spellcasters in the Lost Mine of Phandelver adventure use the evil mage statblock:
(The final boss has a similar feature, and the only other spellcaster statblock used in LMOP is the flameskull, which are undead beings created from the remains of dead wizards.)
Though they use the wizard spell list, they do not necessarily need to follow the rules for PC wizards - NPCs are not built like PCs, and do not need to follow the same rules. Even if they were built similarly, however, even PC wizards only need their spellbook to change their list of prepared spells at the end of a long rest; thus, the enemy need not have such a spellbook on them in order to cast their spells.
The question "How to destroy a spellbook when the wizard dies?" discusses a case in which the querent doesn't want their player's wizard to have access to their NPC wizard's spell list.
As KorvinStarmast's answer points out, Volo's Guide to Monsters provides statblocks for a number of NPC archetypes that are similar to PC classes or subclasses, but as with the above case, the statblocks do not include spellbooks or mention that the NPC requires one.
(Other answers to that question also point out how such spellbooks may have been hidden or set to be destroyed, which could be given as in-universe explanations in case your players reject the out-of-universe explanation that PCs and NPCs are built differently.)