Branch of Topology I have just started to study Topology from M. A. Armstrong's "Basic Topology". Now, I want to know which branch of Topology I can study with this book ? Or is it too early for me to worry about what I like ? If not, which book is good for the next step for me ? Thanks for your comments !
 A: The stuff in that is called point-set topology. While there are some people who do research in it, it's often taken more as a stepping stone to other subjects, such as algebraic topology, rather than for its own right. Even to know that the general field of topology is what you'd want to go into, you should wait until you get deeper into it and into other subjects. 
A: This is exactly the reason the author writes a Preface. This is a quote from the book, with emphasis added by me:

This is a topology book for undergraduates, and in writing it I have had two aims in mind. Firstly, to make sure that the student sees a variety of different techniques and applications involving point set, geometric, and algebraic topology without delving too deeply into any particular area. Secondly [...]

As for your question about "being too early," yes, it is kind of too early to worry about which branch you would specialize in. There's probably still a bit of "breadth" you need to get beyond this book. Judging from this book's contents, it does not cover much of the stuff I would have considered basic topology concerning metric spaces. Maybe you could follow up with something like Topology by Sheldon Davis, which is a pretty trim introductory book that mentions stuff like that.
After a round trip through these two books, you'll probably have an idea of what direction you'd like to explore. You don't have to decide ahead of time.
