How to study real analysis? I am a student of mathematics honours. I am having problem with the Real Analysis portion. I cannot understand how to proceed with the theorems. I donot want to memorize the theorems but want to understand them. But after understanding one theorem, when I go for a theorem which is a little bit tricker one of the same type I have done before I cannot understand how to proceed. I donot know whether is it because my studing technique is wrong or not.Can anyone please help me and suggest me how should I actually study Real analysis then so that i can do well with the theorems and sums?
 A: It is not only about understanding the problem but you should also be able to find the hidden approach to solve it. You should always ask yourself that why only in this way. Does there exist any other proof to this theorem? You should always try to devise your own. Don't just understand the theorem try to analyze them.
One of the main motive to teach Real Analysis is to develop intuition. As in words of Mr. Ittay Weiss:
"You should always use your intuition. If you find that your intuition was correct, then smile. If you find that your intuition was wrong, use the experience to fine-tune your intuition."
Now after understanding and analyzing the result try to find some examples which either prove or disprove the result. After that, study that example very carefully that what it is trying to convey. Make use of your elementary geometry and algebra to interpret it. If there is inequality then try to find that when will equality hold (You will definitely get some interesting results).
The journey of "Real Analysis" is very long and demands a lot of hard work. 
