A nice free book (2nd edition, published earlier this month) by a Physics professor from Sweden, treats the fields and the covariant method:
http://www.plasma.uu.se/CED/Book/
There is also an exercise book with solutions:
http://www.plasma.uu.se/CED/Exercises/
http://www.plasma.uu.se/CED/Book/
There is also an exercise book with solutions:
http://www.plasma.uu.se/CED/Exercises/
