I know that this is supposed to be a primer just to get you "started", but this is pretty much the only book I use anymore, outside of historical books/writings such as the Poetic Edda, RI Page's anthropological study on the Runes, and Tacitus' Germania.
It is a welcome relief compared to all of the wild speculation and liberties that other writers on runes have taken with regard to their esoteric meaning, and the new edition is even nicer than the 2002 release, because it adds several sections on debunking myths as well as additional discussions. (Especially concerning whether or not there is any true evidence runes were used for divination by the Germanic people at all.)
If you need to look beyond the rune poems to get a better grasp on their meanings, this is the book to get. I've found that if the esoteric description in a book about any given rune is longer than maybe about five sentences, it's because the author is starting to make stuff up. The rune poems were 2 to 4 lines. How do people come up with three pages worth of information on what this rune supposedly means? Sweyn's descriptions are clear, concise, and written with proper historical context.
However, this book is much more than simply about the esoteric aspect of the runes. That's just a small part of a very comprehensive, plain-spoken, book about runic history. And like other people have said, it lists other recommended reading materials which are also important.
I made a set of Elder Futhark runes for a friend not too long ago. (Unsolicited gift.) She knows nothing about runes, as far as I know. I knew exactly which book to get her. This one.
I wish this had been around decades ago when I started working with the runes myself. It's much easier to learn the appropriate thing from the beginning instead of having to unlearn a whole bunch of trash.