Learn French: Le sujet de ce livre est intéressant. - The subject of this book is interesting.

This sentence uses the noun le sujet (the subject) to literally say the subject of the book. The expression il s'agit de acts as an impersonal verb phrase meaning it is about. To express a similar idea using the new expression, you could rephrase it as Dans ce livre, il s'agit d'un sujet intéressant (In this book, it is about an interesting subject).

Why is it ce livre and not cet livre?

Ce is the masculine singular demonstrative adjective meaning this or that. You only use cet before a masculine singular noun that starts with a vowel or a silent H (like cet homme). Since livre starts with a consonant, ce is the correct choice.

Does the adjective intéressant agree with the book or the subject?

It agrees with le sujet (the subject), which is masculine singular. While ce livre also happens to be masculine singular, the grammatical core of the sentence is the subject itself. If you were describing a feminine noun, like l'histoire (the story), you would add an -e to the adjective: L'histoire de ce livre est intéressante.