Books by Edred Thorsson are full of reliable Rune information. I recommend Futhark: A Handbook of Rune Magic and Rune Might.
Teutonic Magic by Kveldulf Gundarsson is another good reference.
For a feminine approach to the runes, Freya Aswynn’s Leaves of Yggdrasil or her revised edition renamed Northern Mysteries and Magick: Runes & Feminine Powers is a good reference. This later version includes a CD of Freya activating each rune which is worth the extra price for a new book.
The Little Giant Encyclopedia of Runes by Sirona Knight has an extensive list of attributes to each rune. The presentation of each rune seems to stand alone outside of the Norse Mythology, though there is a simple presentation of the mythos included in the text.
The next text may surprise you, but The Language of the Goddess: Unearthing the Hidden Symbols of Western Civilization by Marija Gimbutas opened my eyes to the universal power and messages contained in the runes. These symbols were used by earliest humans to communicate key information, which seem to be universal in meaning no matter the location. The synergy between these and the Elder Futhark is remarkable and enriches the runecaster’s breadth of understanding. This book reconciled my years of Goddess teachings with my Norse heritage. As a priestess, it gave me more tools to work with the energies of the runes, and understand them at a primal level.