There is not much. That is the first thing to know about learning materials for Icelandic, and it changes how you should read a list like this one.
For Spanish, the problem is choosing. For Icelandic, the problem is that a few things are genuinely good, a lot of things are thin, and the gaps between them are where a learner falls through. The list below is not a competition. It is numbered for ease of reading, not because the fifth thing beats the sixth, and it is an honest map of what there is, what each thing is for, and who it suits. I have used most of it. I have quit some of it, and I say so where it happened, because the failure was usually fit rather than quality.
Prices and availability move. Everything below was checked at the time of writing, and you should check again before you rely on it.
Víkingur. Every lesson is built from how you did on the one before it, rather than pulled from a fixed syllabus. Conversation practice puts you across from someone who speaks first and stays in Icelandic even when you falter, and tapping a word pulls its grammar straight from BÍN instead of a guess.
Icelandic Online, from the University of Iceland. Free, several levels from absolute beginner upward, built by people whose job is teaching Icelandic to foreigners. The closest thing to a complete free course, and the place to start if you have never touched the language. The one drawback any course shares: sitting down to the next unit is a decision you have to keep making.
Íslenska fyrir alla, which translates as Icelandic for everyone. Free workbooks with audio, visual, structured like a proper exercise book, built for adults teaching themselves. Better designed for a self-teaching adult than almost anything else for this language, paid or not. I got further with this than with anything I bought.
BÍN, the inflection database of modern Icelandic, from Árnastofnun. Type in any word, in any form, and it shows every form the word can take. It is the authority. When a textbook and BÍN disagree, BÍN is right.
Íslensk nútímamálsorðabók, the dictionary of modern Icelandic, also from Árnastofnun. Definitions in Icelandic, which is no use in month one and enormous use in month eight.
Snara, the paid dictionary service with the big Icelandic-English dictionaries behind it. Worth it once you are reading real text and the free tools stop being enough.
Complete Icelandic, in the Teach Yourself series. Thorough and well organised. I did not finish it. It moves fast and densely, and the moment I hit something I could not resolve on my own, studying stopped being something I chose and started being an imposition on someone else's evening.
Colloquial Icelandic, by Daisy Neijmann. Its free companion audio is still downloadable from the publisher. Often recommended alongside Complete Icelandic, with a reputation for a more conversational ordering that gets you saying something earlier.
Drops. A vocabulary app, pictures and words, five minutes at a time. Good for exactly what it is, which is getting nouns into your head with a picture attached. It will not teach you a case ending and does not claim to.
Memrise. Community-made Icelandic decks, moved off the main app onto their own site a couple of years ago. Free, uneven, worth a look for the good ones, especially anything built around a specific textbook's vocabulary.
Pimsleur. A short Icelandic course, audio only, listen and repeat. A reasonable way to spend the first month if you learn by ear. It runs out quickly.
Glossika and Mango Languages both currently offer Icelandic. Sentence-based drilling in the first case, a more conventional course in the second. Most of the well-known language apps, including the biggest one, do not offer Icelandic at all.
RÚV, the national broadcaster, especially Krakkafréttir and the wider KrakkaRÚV children's section. Free within Iceland, geo-blocked once you are outside it, so check what actually plays from where you are before building a routine around it. Krakkafréttir is real news in simple sentences, and it is the single most recommended piece of Icelandic input for learners.
Mímir, in Reykjavík. Icelandic courses for foreigners at several levels, evenings included.
The University of Iceland's BA in Icelandic as a second language. A bigger commitment, with its own entrance exam.
Private tutors, at rates that in my experience run from about the price of a nice lunch to the price of a nice dinner per hour, booked around two people's weeks. A room with a teacher does one thing no app or book can, which is put you somewhere you have to speak Icelandic to someone who will not switch.
Two things worth doing that are not on the list because they are not a named thing: any Icelandic text you can read with a dictionary at hand, news sites and recipe blogs and the letters that arrive from the bank and the school, and radio left on in the background, understanding nothing. Both are worth more than they feel like they are while you are doing them.
Plainly, because a list like this should say it.
For a structured course, the free Icelandic Online beats any paid app I have tried. For a self-teaching workbook, the free Íslenska fyrir alla is better designed than the paid books. For grammar reference, the free BÍN is better than anything money can buy, because it is the source the paid things copy from. For input, the free RÚV is the real thing and the rest are imitations.
Where paid things earn their money is in the gaps between those. A teacher who will not let you switch. A dictionary that goes deeper once you are reading real text. Something that writes the next thing for you so that you do not have to decide what to study, on the evenings when deciding is the whole obstacle.
Know what each thing is for, and you will not buy the wrong one. Most people learning Icelandic did not fail for lack of resources. They failed for lack of Tuesday evenings, and no list fixes that.
