Rather than summarizing Kierkegaard's (or should I say, Anti-Climacus') major concepts, I'd like to comment strictly on this particular edition. I am disappointed with Walter Lowrie's translation here - it feels cumbersome and doesn't read as well as it should. While he provides some insightful editorial comments, this is an overall weak effort.
I would highly recommend choosing the Princeton edition translated by the two preeminent Kierkegaard scholars, Howard and Edna Hong. That IS the definitive edition. You'll notice even the title is translated differently as "Practice in Christianity". Seeing as their edition preceded the Lowrie translation, I wonder who even thought a new translation was necessary! I suppose there is a fairly high demand for Kierkegaard's main works in cheap paperback editions, but if you're going to go to the trouble to understand his profound philosophy, you might as well do it the right way with the definitive edition.
It's a bit more expensive, but in addition to a superior and much more readable translation, you get over one hundred pages of supplementary material including, most notably, entries from Kierkegaard's journals and papers pertaining to this work. Don't waste your time on a second-rate edition. Get the real thing.