Íslenska fyrir útlendinga - by Ásta Svavarsdóttir, Margrét Jónsdóttir
"Íslenska fyrir útlendinga" translates to "Icelandic for foreigners" and is (quite literally) an old school book, and has been used as teaching material in the University of Iceland for decades. It first came out in 1988 and has been revised a few times to modernise and it. This revision (and the most recent one) came out in 2009.
Note that this book is in Icelandic so we recommend it only for students of the language that are beyond the beginner stage and can comprehend simple sentences at least.
Note æfingar exercise book comes also with it and included in price, two books.
Check out Árstíðir book for learning Icelandic with simple text.