a qui sont les livres?  Ce sont les miennes.  Why isn't it ces sont les miennes?

Ruth, 

 «ce sont» is the plural form of «c'est». «ce» used in this manner is an indefinite, invariable pronoun that is used mostly, but not exclusively, with «être» (instead of cela/ça). 

Of course «ce» ( ce,cet,cette,ces ) can also be an adjective - «ces» is then the only plural form of the adjective,  and is followed by a noun, not a verb. ‘ Ces ‘ is never a pronoun.

C'est, ce sont = this is, these are (demonstrative pronouns)

demonstrative-adjectives-ce-cet-cette-and-ces-mean-this-that-and-these-those

https://french.kwiziq.com/questions/view/use-of-ce-and-ces

Just to add to Maarten's answer:

Ces is a demonstrative pronoun and always followed by a noun. For example: 

Ces livres sont les miennes. -- These books are mine.

On the other hand, in ce sont, ce is the subject and functions as a noun:

Ce sont les miennes. -- They are mine.