Avoid at all cost the Glendenning one.
This is not a friendly book. The learning curve is so steep that you're up against noun cases, and verb conjugation right at the outset. The supply of sentences which the author requires you to learn rote fashion doesn't inspire the learner to want to learn Icelandic, as to all intents it seems like random and rather useless sentences which would be suited to those with a love of complex grammar and syntax rather than the use of the language for everyday conversation.
As I own this book, pictured with the geysir, church, horses, ships, ravens etc on the front cover, this book's author is P.T. Glendenning. As far as I know, Hildur Jonsdottir has no hand in this earlier Teach Yourself Icelandic example of how not to write a book on learning Icelandic.
On the contrary, Hildur Jonsdottir's modern offering also entitle Teach Yourself Icelandic, has a different cover, being skyblue in colour rather than the garish example above. The HJ version deals with grammar and syntax when needed, and the book aims to furnish the learner with useful everyday spoken Icelandic, if you're planning to go to Iceland for a trip.
Don't confuse the two books.
The earlier Glendenning one is utterly confounding, with excercises that require you to translate into Icelandic words which the chapter hasn't introduced, nor contained in wordlist at the back. You have been warned.
