Correct form of definite article
Which of these is correct: "Hins rauða hundur" or "Rauða hundurinn"? The former is what I see is the old versions of "Teach Yourself Icelandic" (ca. 1970), but the latter is what I see in "Coloquial Icelandic".

Question

Answer

I'm not a native speaker but the common way to use the definite article is via suffix. So you add -[i]nn (male) -[i]n (female) -[i]ð (neuter) to the noun, these are the paradigms in the nominative case. 
But you can place it on the beginning as well. However "Hins" will be used in genitive case, so you rather use "Hinn".

Answer

Lífthrasir is correct but I want to add:
Hins rauða hundur and Rauða hundurinn are not correct gramatically

nominative:  hinn rauði hundur
accusative:   hinn rauða hund
dative:          hinum rauða hundi
genitive:        hins rauða hunds

nominative:    rauði hundurinn
accusative:     rauða hundinn
dative:            rauða hundinum
genitive:          rauða hundsins

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