Learn Hardcore Icelandic: Ég er ánægður með framfarir þínar.

Ánægður is an adjective meaning pleased / happy / satisfied. In Icelandic, adjectives have to agree with the gender, number and case of the noun (or pronoun) they describe.

The pronoun ég (I) itself has no gender form, but the speaker has a gender.
If the speaker is grammatically masculine, the adjective takes masculine singular nominative → ánægður.
So the full idea is: Ég (maður) er ánægður = I (a man) am pleased.

So -ur here is just the masculine singular nominative ending of the adjective.

How would the sentence change if the speaker is a woman (or talking about a woman)?

The adjective changes, everything else stays the same:

Masculine speaker:
Ég er ánægður með framfarir þínar.
Feminine speaker:
Ég er ánægð með framfarir þínar.

If you are talking about someone else:

Hann er ánægður með framfarir þínar. – He is pleased with your progress.
Hún er ánægð með framfarir þínar. – She is pleased with your progress.

In all of these, ánægður / ánægð agrees with the person who is pleased, not with progress.

What does með do here? Why ánægður með and not some other preposition?

Með is a very common preposition that can mean several things, depending on context and the case it takes.

In this sentence it introduces what you are pleased about:

ánægður með e-ð = pleased with something

So:

Ég er ánægður með framfarir þínar.
I am pleased with your progress.

Here með takes the accusative case (see below). Other common patterns with ánægður:

ánægður með e-n / e-ð – pleased with someone / something
ánægður með það að… – pleased that…
e.g. Ég er ánægð með það að þú lærir íslensku.
I’m pleased that you’re learning Icelandic.

What case are framfarir þínar in, and why?

Framfarir þínar is in the accusative plural feminine.

The noun framför (progress, improvement) has plural framfarir.
The phrase ánægður með normally takes an object in the accusative.
Feminine accusative plural of framför is framfarir (same form as nom.pl.).
The possessive þínar is also feminine accusative plural, agreeing with framfarir.

So:

með + framfarir þínar → with your progress (grammatically: preposition + acc.pl.fem. + agreeing possessive).

Why is framfarir plural? In English progress is uncountable.

Icelandic and English don’t always treat the same concepts as singular or plural.

Framför (sg.) / framfarir (pl.) literally means advance(s), improvement(s).
When talking about someone’s general improvement, Icelandic usually uses the plural:
- Ég er ánægður með framfarir þínar.
  I am pleased with your (improvements / progress).

You’ll very often see framfarir (plural) used where English uses uncountable progress.

Why is þínar after framfarir instead of before it? Could you say þínar framfarir?

Both word orders exist, but they are not equally common or neutral:

framfarir þínar – the most usual, neutral order in everyday speech and writing.
þínar framfarir – possible, but tends to sound more emphatic or contrasty, like your progress (as opposed to someone else’s).

In Icelandic, the normal position for possessive pronouns like minn, þinn, hans, hennar is after the noun:

bókin mín – my book
vinir okkar – our friends
framfarir þínar – your progress

Putting the possessive before the noun often adds emphasis or a slightly more marked tone.

What exactly is the form þínar? How does it agree with framfarir?

Þínar is a form of the possessive adjective þinn (your, singular). It declines like an adjective and must agree with the noun it modifies in gender, number and case.

Noun: framfarir – feminine, plural, accusative
Possessive: þínar – feminine, plural, accusative form of þinn

Some key forms of þinn (singular you):

Masculine: þinn (sg.nom.), þínir (pl.nom.)
Feminine: þín (sg.nom.), þínar (pl.nom./acc.)
Neuter: þitt (sg.nom./acc.), þín (pl.nom./acc.)

So here þínar matches framfarir exactly: fem. + pl. + acc.

Could I say Ég er ánægður með þínar framfarir instead?

Yes, Ég er ánægður með þínar framfarir is grammatically correct, but the nuance shifts a bit:

Ég er ánægður með framfarir þínar. – neutral, standard.
Ég er ánægður með þínar framfarir. – more emphatic on “your”:
- I am pleased with *your progress (in particular / not someone else’s).*

So you can use the preposed version if you want to stress whose progress you’re talking about, but for a simple, neutral statement, the original word order is more natural.

How would I make this sentence negative?

You insert ekki (not) after the verb er:

Ég er ekki ánægður með framfarir þínar.
I am not pleased with your progress.
For a female speaker:
Ég er ekki ánægð með framfarir þínar.

Basic pattern: Ég er (ekki) + adjective + með + object.

How would this sentence look in the plural, e.g. “We are pleased with your progress”?

The verb and adjective change to plural, but the object phrase stays the same:

To one person (singular your):
- Mixed / male group:
  Við erum ánægðir með framfarir þínar.
- All-female group:
  Við erum ánægðar með framfarir þínar.
Here ánægðir / ánægðar agrees with við (we).
To several people (plural your), you’d normally use ykkar instead of þínar:
- Við erum ánægðir með framfarir ykkar.
  We are pleased with your (plural) progress.

How do you pronounce the tricky parts like Ég, ánægður, þínar?

Approximate guides for an English speaker:

Ég – roughly like “yeh” but with a long vowel: [jɛː] (often the final g is very soft or almost silent).
er – like “air” but shorter: [ɛr].
ánægður – approximately “OW-nai-thur”:
- á = ow in now.
- næg = nai.
- ð = the soft th in this (often quite weak).
- Final ur is short, with a rolled or tapped r.
framfarir – roughly “FRAM-far-ir”, stress on the first syllable, rolled r.
þínar – roughly “THEE-nar”:
- þ = unvoiced th as in think.
- í = long ee as in see.
- Final ar with a tapped/rolled r.

Exact Icelandic pronunciation is more precise than this, but these approximations will make you understandable.