When I first decided to begin real analysis I had a look at the much recommended book 'Principles Of Mathematical Analysis' by Rudin, however I found it very complicated and understood very little of it. I instead chose to use a combination of Ross and Bartle to learn from and it has been much clearer. I decided yesterday to have another look at Rudin's book and I seem to understand it a lot better and can follow it. The only difference is that the books I'm currently using don't use metric spaces. Should I stop using the ones that I am and just use Rudin, or should I finish Ross and then move on to Rudin afterwards for a more advanced treatment.
Should be noted that I am self teaching this subject.
As an ancient theacher I suggest: take real line as given, and look to approximation and limits. Ask yourself:"which problem are I solving with such machinery".Then pass from the line to the plane, end so on. Ask yourself "why functional analysis" and go on. Do't be hurry: it takes several years. Bye