Here you will find lists of useful resources of different types. In general the most useful ones are at the top of each list.

Dictionaries

Orðabók (Wordbook) - this online dictionary is subscription only, but is my favourite way to look up words. Works great on smartphones. Excellent value for money.

Textbooks

Íslenska fyrir alla (Icelandic for all) - my favourite text, used by people who have moved to Iceland. Entirely in Icelandic without any English explanations, with excellent quality audio clips. Emphasis on ordinary speech in everyday situations.