Reccomendation for Abstract Algebra I am familiar with BASIC calculus of single variable,multivariable,linear algebra,ordinary differential equations,.I HAVE NOT BEEN INTO RIGOROUS PROOFS .If someone can let me know book(s) which goes from basic to advanced level and contains lots of solved examples and exercises for self study .Also any online study material useful for this purpose will be great .I will be obliged .Thanks
NOTE :- I am not a Maths Major and has never been to college for studying Maths ,But studied from online sources available 
 A: To preface, my recommendation is NOT an online resource but it is truly an excellent book for teaching yourself abstract algebra.  It's called "A Book of Abstract Algebra" by Charles C. Pinter.  The book moves fairly slowly and is designed for someone who is not all that familiar with proofs.  It's very easy to read, and also has many, many exercises to be worked out.  Also, it's published through Dover which is well known for having very cheap books.  I'm hoping that your situation actually allows you to attain a physical copy.  There are many great online resources, but I've been really impressed with this book as an introductory text.
A: You can read this book. It is free.
You will learn about type of proofs, the logical reasoning and the basic set theory in order to do maths. Here the direct link.
A: It is typical (thought certainly not the only way) to transition to higher math through real analysis. The link below will give you a complete text of lectures by Vaughan Jones (a Fields Medal winner) that starts from the basics and builds. 
It is self-contained and the material is clearly presented:
https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxtYXRoMTA0c3AyMDExfGd4OjJiNTJkM2M2ZWUzZGIwYWQ
