TITLE: Branch of Topology
QUESTION [5 upvotes]: 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 !

REPLY [8 votes]: 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.