I started this book on the plane to Dublin and finished it a day after I had arrived. It was an excellent complement to the city itself and a great introduction to the early writing and thinking of Joyce, and definitely an easier task than starting by jumping head-first into Ulysses or Finnegan's Wake.
My recommendation for the order of Joyce books to read: Dubliners, A Portrait of the Artist as a Young Man, Ulysses, Finnegan's Wake (in order of difficulty and chronologically too, I think). I am leaving out at least one but those are the essential works.
Dubliners was his first work, written as he walked the streets of Dublin and observed its people before leaving it, saying it was too 'provincial' from what I remember. After that his experimentations in writing and language began, epitomized by pretty much everything else he wrote. Anyway, if you want to write, if you want to think, if you're interested in literature, if you're interested in Ireland, you need to read Joyce, and this is where Joyce starts.