Icelandic has two possessive pronouns: minn (my) and þinn (your).

They inflect (change) depending on what it is you possess, and the possession can sometimes have the definite article (the word the in English), depending on the kind of thing you possess and how formal or informal you want to sound. 

That sounds complicated. Let’s make it a little easier!

As a side-note: there are other ways to indicate possession in Icelandic, notably with:

• the reflexive possessive pronoun sinn (like his own, her own, their own, etc. in English); 
• the personal pronouns in the genitive case (like his, her, our, etc. in English), and with 
• any noun in the genitive case (like apostrophe 's in English).

Gender

The words minn and þinn inflect, depending on whether the thing you own is (grammatically) masculine, feminine, or neuter. It doesn’t matter if the owner is a man, woman, or anything in between.

Notice that minn and þinn are always identical to each other, except for the first letter, m or þ. 

• Þetta er sonur minn, þetta er dóttir mín, og hérna er húsið mitt > This is my son, that is my daughter, and here is my house.
• Sonur þinn er myndarlegur, og dóttir þín er mjög dugleg! Húsið þitt er drasl, samt > Your son is handsome, and your daughter is very industrious! Your house is shit, though.

Notice the word order, too. The pronoun comes after the possession: it’s not my son, it’s son my; it’s not my house, it’s the house my. I’ll go into why it’s the house below.

Case 

Like most pronouns, minn and þinn also inflect with case (nominative, accusative, dative, and genitive). Check out Basics of Cases if you’re unsure about how cases work in general.

To learn how to decline nouns I recommend Brian Casper’s YouTube channel, Icelandic For Foreigners, starting with this video.

• Hefurðu séð töskuna mína? Ég týndi töskunni minni > Have you seen my bag? I lost my bag.
• Geturðu gefið kettinum mínum að borða meðan ég er í burtu? > Can you feed my cat while I’m away?
• Ég hlakka til útgáfu bókarinnar þinnar > I look forward to the publishing of your book.

Number 

Minn and þinn also inflect with number, of course.

Notice that the dative and genitive is the same across all genders in the plural. Makes it easier to learn! I've gone ahead and boxed those together to make that easier to see.

• Er þetta pakkinn þinn? Ég hélt að pakkarnir þínir væru stærri > Is this your present? I thought your presents were bigger.
• Hefurðu séð töskurnar mínar? Ég týndi töskunum mínum > Have you seen my bags? I lost my bags.
• Geturðu gefið köttunum mínum að borða meðan ég er í burtu? > Can you feed my cats while I’m away?

The Definite Article 

You often (but not always) use the definite article (the word the in English) with the thing you possess, and it depends on what type of possession you’re talking about. There are four types of possession.

1. Concrete nouns (something physical: a boy, the wind, a hovercraft)
2. Abstract nouns (something non-physical: an idea, an opinion, shame)
3. Relations (words like mom, co-worker, friend)
4. Body parts (heart, back, leg)

• Bíllinn minn er ’77 módel > My car is a ’77 model.
• Hæfileikar mínir felast fyrst og fremst í því að rata í vandræði > My talents are first and foremost about finding trouble.
• Ég talaði við vin minn um fjölskyldu mína > I spoke to my friend about my family.

Possession of body parts is a bit different; ordinarily, you probably shouldn’t use minn or þinn with those. You can check out Possession and Body Parts for an in-depth dive into that.

The Colloquial Style Is Simpler

Man, four different types of words being treated differently sounds really complicated. You can make it simpler by just mastering the colloquial style. That’s what you would use in regular day-to-day talk with friends and family. I wouldn’t use it if you’re writing an academic paper or something fancy like that, though.

The language is constantly evolving. There is a trend to generalise the rules for concrete nouns and use the definite article with abstract nouns and body parts (not relations, though; that would still sound crazy).

•  Ég gleymdi símanum mínum > I forgot my phone.‍
• Jæja, segðu okkur frá hugmyndinni þinni > Well, tell us about your idea.
• ‍Ég ætla að bursta hárið mitt > I’m going to brush my hair.‍
• Hringdirðu í mömmu mína? > Did you call my mom?

Conversely, if you want to be extra formal, you can treat ALL words like abstract nouns and skip the definite article. Don’t do this in casual conversation, though, or you’ll sound stuffy.

• Bók þín, Bráðin, kom út núna nýlega > Your book, The Prey, came out recently.
• Líf mitt hefur ekki verið neinn dans á rósum > My life has not been a walk in the park (literally: a dance on roses)
• Yfirmaður minn er óþolandi > My boss is insufferable.
• Höfuð mitt er að klofna í sundur! > My head is cleaving in twain! (it‘s pretty formal, guys)
  

Summary

Minn and þinn inflect, like most pronouns. If you’re a beginner, focus on just the gender in the nominative singular. Then later add in case and number.

The definite article plays a role in possession. If you’re a beginner, or if you’re just aiming for spoken fluency, just master the colloquial style.‍

If you have high ambitions, such as for academia or politics, I salute you! Get good at everything.