"What I want to do is read this book."
Is it correct? Or, can I say:
"What I want to do is to read this book."
"What I want to do is reading this book."
Are all of the three sentences correct?
The infinitive read
This is what's called a Wh-Cleft sentence (also "Pseudo-Cleft"); it's a variety of Clefting, which is a syntactic device to emphasize certain parts of sentences. Clefts come from simple sentences like
which they then proceed to dissect into parts, add various markers, and mix'n'match, viz.
These are all grammatical, and they all mean the same thing, which is
The reason why read and not reading is correct here is that want takes an infinitive complement, not a gerund. Do is an infinitive, so read has to be an infinitive, too.
If you use a cleft construction, you have to remember what the main verb is, and match it up correctly. Even when it's been moved away, the verb still governs what kind of complement it takes. That's one of the costs of complex constructions.