How many parts does Walter Miller Jr.'s novel "A Canticle for Leibowitz" have?

A Canticle for Leibowitz has three parts:

1. Fiat Homo - Let there be man
2. Fiat Lux - Let there be light
3. Fiat Voltunas Tau - Let thy will be done

The book is set after a nuclear war has badly damaged the world. Science is prohibited.

• In the first part of the book, a monk in 26th century discover a fallout shelter with notes and tries to preserve them. This are the writings of Leibowitz. This is akin to the dark ages
  
• The second part of the book is similar to the Renaissance, with the rise of secular teachings and a struggle between the church and state in its infancy.
  
• The third part of the book is set in a more modern time. The world is again in a nuclear age. There are also starships. Eventually, a nuclear war occurs again.

Miller has two predominant themes in his book, the church vs. state and the repetition of history.