Two very useful textbooks for learning Old Icelandic are available (at this writing) for free in PDF form. The first is A New Introduction to Old Norse, Part 1: Grammar available at http://www.vsnrweb-publications.org.uk/NION-1.pdf. The second is the accompanying text, A New Introduction to Old Norse, Part 2: Reader: http://www.vsnrweb-publications.org.uk/NION-2a.pdf.

 

You can also purchase printed copies of the above texts from various commercial vendors.

 

Rob