Here are some resources that I’ve found useful for the study of Icelandic:

Once you’ve decided to learn Icelandic, you’ll naturally start looking for some self-study material. The books you’re most likely to encounter are:

Teach Yourself Icelandic / Complete Icelandic, by Hildur Jónsdóttir
This is probably the best one to start with if you are completely new to Icelandic, or to learning languages on your own. The audio accompanying the book is read at a slower than normal pace, with good annunciation, which helps when you are just starting out and trying to catch the pronunciation correctly.

The latest edition is called Complete Icelandic, but there aren’t many changes compared to the previous edition which has the title Teach Yourself Icelandic. The audio dialogues are identical, and aside from some formatting changes and the addition of a summary at the end of each chapter, the text is pretty much the same.

Colloquial Icelandic, by Daisy L. Neijmann
This is another very good book, but definitely more challenging, with most of the audio being read at normal or near-normal speed. The material is also a lot denser, so you cover quite a bit of vocabulary and grammar in each chapter.

Íslenska Fyrir Alla
The material in this collection is completely in Icelandic, but if you’ve made it even partly through either of the two books above, you should be fine. I wasn’t sure about it at first, but really came to like the entire series. It is definitely geared toward newcomers to the country, and deals with situations you would encounter as a foreigner living in Iceland.

Learning Icelandic
This is another good beginning Icelandic book, with CDs and a companion book filled with grammar exercises (with an answer key). One feature of the main text is the 60-page grammar which is one of the best beginner grammars that I’ve encountered.

This is a good intermediate book, consisting of a series of short texts of increasing difficulty, by various Icelandic authors. There are also exercises to test your comprehension and give you writing practice.

Íslenska fyrir útlendinga
This is an Icelandic grammar book written completely in Icelandic, so is good for intermediate students. You don’t just learn about Icelandic grammar, you learn how to talk about it in Icelandic. An excellent resource. There is also a companion book with exercises.

Icelandic: Grammar Texts Glossary, by Stefán Einarsson
This is a somewhat old text, but the grammar coverage is still some of best you’ll find. The texts are a little archaic, but valuable nonetheless as a source of vocabulary. A good supplement for the serious student.

Íslensk-Ensk Orðabók
There aren’t a ton of Icelandic-English dictionaries to choose from, and this one does a pretty good job. I picked up a copy on my first trip to Iceland 🙂 It is also available online as part of the University of Wisconsin Digital Collections, which has been incredibly helpful for looking up words while reading Icelandic news sites.

The oldest and largest bookseller in Iceland. I’ve ordered from them a couple times so far, and have gotten my books within a week or so, with very good packaging.

Largest publisher in Iceland; I’ve ordered books from them as well with an equally good experience.

Beygingarlýsing íslensks nútímamáls
Excellent site for finding conjugations or declensions of words, from the Árni Magnússon Institute for Icelandic Studies.

Viltu læra íslensku?
A series of 21 video episodes, each broken into two parts – first a short skit showing a daily situation, like going to the bank or the pool, then a classroom lesson. The stories are a little corny, but it’s a good resource for listening comprehension.

Icelandic Online
A free course from the University of Iceland, with lots of short lessons/drills and audio.

A good site for basic grammar reference, covers most all aspects that you’ll encounter when starting out.

Over 100 of the most common Icelandic verbs, conjugated and with examples. – Nordic Languages
A forum discussing Nordic languages with frequent discussion of Icelandic topics, including responses from native speakers.

A few news sites that I check out on a regular basis.

The website of the the Icelandic National Broadcasting Service. You can read the news in Icelandic, as well as watch the daily newscasts online.

Website of one of Iceland’s largest daily newspapers.

News, video, radio…a lot of media resources.

An Icelandic weekly newspaper. You can download the issues in PDF format for offline viewing.