This should have been called "An Old Norse Reader" rather than "An Introduction to Old Norse," for it assumes more than some beginning students might be able to handle. Despite the valid criticism of the above reviewer, however, I was surprised by how quickly I was able to read The Vineland Sagas in Old Norse after just a perusal of the grammatical overview found at the back of this book. Each word in Old Norse is found in the Glossary so you will be able to find the meaning of all the words one reads, but it would have been more efficient to have placed the meaning of the more difficult words alongside the text as is often done by recent Readers. The selection of Old Norse readings is broken up into West Norse, primarily, but not exclusively, Old Icelandic and Old Norwegian texts and East Norse, primarily comprised of some very interesting Old Swedish texts. You might be surprised to see how similar East Norse is to Gothic. More and more Old Norse sagas are available in full online, but if you want a handy Old Norse reader with a very fine smorgasbord of texts, then this is the book for you. Gordon first offers parts of Snorri's Edda describing the death of the gods at Ragnarok and then parts of The Vineland Sagas detailing the discovery of America and then some other famous texts such as Thormod's poem and account of the battle of Stiklestad where Holy King Olaf fell that is part of the still untranslated Fostrbraedra Saga. Other accounts describe the settling of Iceland, a Norwegian's trek to Greenland to acquire a polar bear, Hrafnkells Saga in full, the famous Burning of Njal, and excerpts from Snorri's Heimskringla and the battle of Stamford Bridge that effectively ended the Viking age.
But if you are serious about learning Old Norse you will have to track down the justly praised Vallfells and Cathey's "Old Icelandic: An Introductory Course" (Oxford University Press, 1981)and the most learned dictionary is Cleasby and Vigfusson's "An Icelandic-English Dictionary" (Oxford, 1874) that includes both Old Norse and Modern Icelandic. More student and reader friendly is the still in print "Concise Dictionary of Old Icelandic" by Zoega (1911). If you are not willing to buy an expensive copy of Vallfells and Cathey, but are interested in seeing Old Icelandic declensions given in great detail and don't mind some German, then see Adolf Noreen's "Altislaendische und Altnorwegische Grammatik" (1923) that is in print. Gordon considered it the chief authority on Old Norse grammar and Orrin Robinson also recommends Noreen in "Old English and Its Closest Relatives" in his comparative linguistic survey of Old Norse.
Please know that Cleasby and Vigfusson's dictionary, Zoega's dictionary and Noreen's grammar are also available online at the Germanic Lexicon Project of U Penn. Amazon.com.uk also offers a 3 part Old Norse grammar at a reasonable price, though it is still not as thorough as the teutonic Noreen.
One might also consider learning Old Norse by way of modern Icelandic since the language has not changed a great deal. Stefan Einarsson's "Icelandic Grammar" of 1945 is a suitable introduction to Modern Icelandic grammar with accompanying readings on topics that are somewhat out of date. Mal og Menning (Language and Culture), Iceland's premier bookstore, located in Reykjavik offers more up to date - as recent as 2000 and 2002 - resources for learning modern Icelandic.