I was thinking of buying the book mentioned in the title and wanted to find out the non number theory prerequisites for it (I’ve found no information at all regarding that).
If I may request that you be specific as to how much of a certain topic or course I may need. In other words use terms like “elementary definitions in set theory” instead of “set theory” (if that is the case). My math background is made up mostly by the courses I’ve taken so far in my CS degree: calc 1&2, linear algebra 1&2, probability, statistics, discrete mathematics, mathematical logic and ordinary differential equations.
I wasn't familiar with this book before seeing your question, but having looked through it, I would say it is aimed, particularly starting in its middle chapters, at readers with a much higher level of sophistication than you describe. In terms of both specific facts and overall mathematical maturity, I would say the book requires one to have had introductions to analysis and abstract algebra roughly at the level of Rudin's Principles of Mathematical Analysis and Artin's Algebra. A knowledge of the residue calculus (part of beginning complex analysis) is necessary for some of the later material.
For someone with your level of preparation, a book like Stark's An Introduction to Number Theory might be more appropriate. Other recommendations can be found here.