I have been studying statistics for the past two years. Almost everything I have learnt is about parametric statistics. Now I would like to learn more about non-parametric statistics. Can anyone suggest some concise (perhaps readable as well) introduction into this area?
It depends on what you mean by 'concise', what kind of level of treatment you're seeking (including mathematical vs concepts and intuition), what techniques you want included.
I'd strongly suggest starting with books, and reading more than one book.
Conover's "Practical Nonparametric Statistics" is good, and one I'd definitely lean toward including in any list.
Daniel's "Applied Nonparametric statistics" is very good, reasonably comprehensive for its size.
I found Neave and Worthington's "Distribution-Free tests" very readable when it first came out (and in many ways it still is). Nowadays the code in it looks somewhat dated, but on the other hand, it's generally readable enough to translate. If you can find it it's a good introduction; a worthwhile one to pick up second hand if you don't buy it new.
There are dozens of good books, some older than the three I mentioned, some newer; some may well suit you better than any I've mentioned. I'd start with a university library and browse around on searches with terms like in the above titles, and if possible, see what's nearby.
Read through a few of them and find several you like.
When I did nonparametrics as an undergrad, there were something like eight books in the recommended reading, perhaps more. Every single one of them had something most of the others lacked. I'm glad I had a look at all of them.
If your field of study is in the soft sciences (e.g., psychology, sociology, education), I would recommend Nonparametric Statistics for the Behavioral Sciences by Siegel and Castellan (McGraw-Hill Book Company). (I have the second edition from 1988). From the preface:
A distinctive feature [is] the step-by-step outline of application of each procedure to actual data.
I was surprised not to see Larry Wasserman's All of Nonparametric Statistics mentioned.
I think it is a great book of relative concise size. Especially if someone already has some background in parametric Statistics this book offers a very fresh look on "statistical methods that aim to keep the number of underlying assumptions as weak as possible". I found it less wordy that other introduction/primer books; this can be a good or a bad thing depending on one's preferences. The only "delta" this book has it is that it does not really cover rank tests.
I found "Semiparametric Regression" by Carroll, Wand et al. to be quite readable. It is outdated, but a good thing to start before moving on to Simon Wood's concise, but dense, book on GAMs.
Both these books focus on penalized spline regression models, which isn't everything in nonparametric stats. But arguably most useful for applied people.