Learn French: Tu peux choisir n'importe quel livre.

The phrase n'importe quoi means anything when it stands completely alone as a pronoun. But in this sentence, the word any is describing a specific noun (livre). When you put any directly in front of a noun to offer a free choice, you must use the adjective phrase n'importe quel instead.

Does the quel part of n'importe quel change depending on the noun?

Yes! Because n'importe quel acts as an adjective, the quel part must match the gender and number of the noun it modifies. Since livre is masculine singular, we use quel. If you were talking about a feminine noun like pomme (apple), you would say n'importe quelle pomme.

Could I use tout instead of n'importe quel to say any?

Not really. While tout can sometimes mean any or every when stating broad facts, n'importe quel strongly emphasizes free choice. It means any book at all, it doesn't matter which one, making it the natural phrasing when telling someone they can pick whatever they want.

Why is choisir left in its infinitive form?

Choisir (to choose) stays unconjugated because it directly follows another verb that is already conjugated. In French, when you have a modal verb like pouvoir (can or to be able to) conjugated as tu peux, the action verb that comes right after it always stays in its dictionary form.