The book of Isaiah is so named because it contains the prophecies of Isaiah.
It is a beloved book due to its many glowing promises about the future and frequent allusions to the future ministry and work of Jesus. As such, it is not surprising that Isaiah is one of the four most quoted books in the New Testament (the others are Deuteronomy, Psalms, and Genesis).
Isaiah lived in the 700s BCE, his life and ministry spanning the reigns of several kings of Judah. His message was one of repentance, which he faithfully continued even though he was convinced that the people wouldn’t respond to his warnings.
A basic outline of the book is:
The first 35 chapters (1-35) contain Isaiah’s prophecies.
Chapters 36 through 39 are historical references.
In chapters 40 though 55 the exile of Judah is covered.
The concluding chapters (56-66) address the time after the exile, when the people return home.