The course does not have a required textbook.  Here are links to some useful textbooks (you will need to be on campus to access some of them).   

 

Marcus, Number Fields

This has been recommended to me.  It is a apparently good for beginners and has lots of exercises.   Chapter 1 is motivational and can be skipped if desired.  It avoids local fields and Dedekind domains.

 

Neukirch, Algebraic Number Theory

This text is more advanced and treats the subject from the general point of view of arithmetic geometry (which may seem strange to those without the geometric background).

 

Milne, Algebraic Number Theory

Milne's course notes (in several subjects) are always good.

 

Lang, Algebraic Number Theory

 

Murty, Esmonde, Problems in Algebraic Number Theory

This book was designed for self study.  Lots of exercises with full solutions.

 

Janusz, Algebraic Number Fields

 

There are several other references I could suggest if you want to learn something specific (just ask!).   The point is to find a book that works best for you.