Després de córrer, m'agrada seure una estona i mirar el riu.

Because in Catalan, after després de meaning after, you normally use an infinitive when the subject stays the same.

So:

• després de córrer = after running
• literally: after to run

This is different from English, which usually uses the -ing form after after.

More examples:

• Després de menjar = after eating
• Després de treballar = after working

Després de means after.

It can be followed by:

• a noun: després de la feina = after work
• an infinitive: després de córrer = after running

So in this sentence, it introduces the action that happens first: running.

The accent in córrer helps show the correct stress.

Without the accent, Catalan stress rules would suggest a different pronunciation. The accent tells you that the stress falls on the first syllable:

• córrer

For a learner, the important thing is: this is the normal correct spelling of the infinitive to run.

Catalan uses agradar differently from English to like.

The structure is more like:

• m'agrada... = it is pleasing to me...

So:

• m' = to me / me
• agrada = is pleasing

That is why m'agrada means I like in natural English, even though the grammar works differently.

For example:

• M'agrada el cafè = I like coffee
• M'agrada llegir = I like reading

Because m'agrada is the shortened form of em agrada.

In Catalan, the pronoun em often becomes m' before a vowel:

• em agrada → m'agrada

This is just a normal sound-and-spelling contraction, like making the sentence flow more naturally.

Because the verb agrees with the thing that is liked, not with the person who likes it.

Here, the thing being liked is the whole action:

• seure una estona i mirar el riu

That whole idea is treated as a single unit, so Catalan uses singular agrada.

Compare:

• M'agrada llegir = I like reading
• M'agrada seure i mirar el riu = I like sitting and looking at the river

But:

• M'agraden els llibres = I like books

There, els llibres is plural, so you get agraden.

Seure means to sit or to sit down.

In this sentence, it means something like:

• to sit for a while

So:

• m'agrada seure una estona = I like to sit for a while

It is the infinitive form, because it comes after m'agrada.

Una estona means a while or for a little while.

It is a very common Catalan time expression for an unspecified short period.

Examples:

• Espera una estona = Wait a while
• Vaig seure una estona = I sat down for a while

It does not give an exact length of time; it just suggests a short, relaxed period.

Because mirar normally takes a direct object in Catalan.

So Catalan says:

• mirar el riu = to look at the river / to watch the river

English needs at in look at, but Catalan does not use a preposition here.

Compare:

• Mira el mar = Look at the sea
• Miro la finestra = I look at the window

So mirar el riu is the normal structure.

Because one m'agrada can govern more than one infinitive.

Here, the speaker likes doing both actions as part of one idea:

• seure una estona i mirar el riu

So Catalan does not need to repeat the verb:

• M'agrada seure una estona i mirar el riu

You could repeat it for emphasis, but normally you would not:

• M'agrada seure una estona i m'agrada mirar el riu
  This is grammatical, but less natural unless you want emphasis.

It is placed first to set the scene: after running.

Catalan often puts time expressions at the beginning when they give the context for the main idea.

So this sentence first tells you when, and then tells you what the speaker likes to do.

The comma is also natural here, because Després de córrer is an introductory phrase:

• Després de córrer, m'agrada...

You could also move it later:

• M'agrada seure una estona i mirar el riu després de córrer

But the original version sounds very natural.