If you start an airbus course concentrating on just one system is probably not a good idea. The FCOM has all the system information, although it is still a horrible mess compared to other manufacturers. That said, up to date information from the company you do your training with is the most relevant thing.
A book i personally found useful for my A320 course was „Airbus A320 An Advanced Systems Guide“ from Ben Riecken on iBooks. The original airbus CBT was basically nothing but an extended A320 commercial with little practical value. However, the primary reference should always be the documentation given, especially FCOM, FCTM and if they have it, the OMB as the most important manual.