Learn Hardcore Spanish (Spain): Agradezco haber salvado a mi hermano del accidente. - I am grateful to have saved my brother from the accident.

salvar = to save (the action in general or in the future)
- Quiero salvar a mi hermano. = I want to save my brother.
haber salvado = to have saved (a completed action in the past)
- Agradezco haber salvado a mi hermano. = I am thankful to have saved my brother.

So the sentence expresses gratitude for something that has already happened and is completed.

Why does Spanish use haber salvado here instead of just salvar?

Because the saving already happened before the moment of speaking. The speaker is looking back on a finished event.

Compare:

Agradezco salvar a mi hermano.
This sounds strange in standard Spanish, because salvar here feels more like a general or future action (I’m thankful to save him, as a general rule or intention).
Agradezco haber salvado a mi hermano.
Natural: I’m thankful that I managed to save him (in that situation).

So haber salvado clearly locates the action in the past and completed, which matches the idea of gratitude for something that has already occurred.

Who is the subject of haber salvado? Is it the same as the subject of agradezco?

Yes. The subject of haber salvado is the same as the subject of agradezco, which is yo (I), even though yo is not said explicitly.

(Yo) agradezco haber salvado a mi hermano.
= I am thankful to have saved my brother.

The infinitive haber salvado does not show its own subject. In constructions like this, its subject is usually understood from the main verb:

Lamento haber llegado tarde. = I regret having arrived late.
Espero haber ayudado. = I hope to have helped.

In all of these, the subject of the infinitive is the same person as the subject of the main verb.

Could I say Agradezco que salvé a mi hermano instead? Why or why not?

In standard Spanish, no. That sentence sounds wrong for two reasons:

After agradezco que, Spanish normally requires the subjunctive, not the indicative.
Even with subjunctive, Spaniards prefer a slightly different structure.

More natural alternatives:

Agradezco haber salvado a mi hermano.
(Infinitive structure: the one you have)
Agradezco que haya salvado a mi hermano.
Literally: I am thankful that I have saved my brother.
This is grammatically correct, but when the subject is the same (I thank / I have saved), speakers often prefer the infinitive: haber salvado.

If you clearly change the subject, you must use que + subjunctive:

Agradezco que mi hermano me haya salvado.
I am thankful that my brother saved me.

When should I use agradecer + infinitive (haber salvado) vs agradecer que + subjunctive?

Use agradecer + infinitive when the subject of both actions is the same person:

(Yo) agradezco haber salvado a mi hermano.
I thank / I’m grateful to have saved my brother.
(I = the one who thanks, I = the one who saved.)

Use agradecer que + subjunctive when the subject of the grateful feeling and the subject of the action are different:

Agradezco que me hayas ayudado.
I’m thankful that you have helped me.
Agradecemos que hayáis venido.
We are thankful that you (plural) have come.

So:

Same subject → infinitive
Different subject → que + subjunctive

Why is it a mi hermano and not just mi hermano after salvado?

Because of the “personal a” in Spanish.

When a direct object is:

a specific person, or
a pet (often treated like a person),

Spanish normally uses a before it:

Veo a mi hermano. = I see my brother.
Ayudé a mi madre. = I helped my mother.
Salvé a mi hermano. = I saved my brother.

This a does not mean “to” here; it’s just the marker of a personal direct object. In English we don’t say “I saved to my brother”, but in Spanish you must say salvar a mi hermano.

What does del accidente mean exactly, and how does it work grammatically?

Del is the contraction of de + el. So:

del accidente = de + el accidente
literally: “from the accident”

Here de expresses the idea of “from” / “out of” / “away from” a danger or situation:

salvar a alguien del fuego = save someone from the fire
rescatar a alguien del peligro = rescue someone from danger
haber salvado a mi hermano del accidente = to have saved my brother from the accident

So the structure is:

salvar a [person] de(l) [danger / situation]

Why do we say del accidente and not desde el accidente?

Because de (→ del) expresses removal or protection from a danger, while desde usually expresses a starting point in space or time.

salvar a alguien de(l) accidente
= save someone from the accident (prevent them from being affected by it)
desde el accidente
= “since the accident” / “from the accident (in terms of starting point)”

Examples with desde:

Desde el accidente, tiene miedo a conducir.
Since the accident, he is afraid of driving.

Using desde el accidente in your sentence would change the meaning and wouldn’t be natural. You need de / del to express “from (a danger)”.

Could I say de el accidente instead of del accidente?

No. In Spanish, de + el must contract to del (when el is the masculine singular article):

de + el accidente → del accidente
de + el coche → del coche

You only keep them separate when el is not an article but a pronoun or a part of a name, e.g.:

Hablo de él. (él = “him”)
Voy a la estación de El Escorial. (El Escorial is a proper name)

Here el accidente clearly uses el as the regular article, so the only correct form is del accidente.

Can Agradezco haber salvado a mi hermano del accidente mean “I’m thankful that my brother saved me from the accident”?

No. In the given sentence:

The person who is thankful = yo (implied by agradezco)
The person who did the saving = yo (implied subject of haber salvado)
The person who was saved = mi hermano

So it only means:
I am thankful to have saved my brother from the accident.

If you want “I’m thankful that my brother saved me”, you must change the structure:

Agradezco que mi hermano me haya salvado del accidente.
(my brother = subject of haya salvado; me = object)

Word order and pronouns are crucial for who saved whom.

Could I replace a mi hermano with a pronoun? What about haberlo salvado or haberle salvado?

Yes, you can replace a mi hermano with a direct object pronoun:

Agradezco haberlo salvado del accidente.
= I’m thankful to have saved him from the accident.

In most standard grammar explanations:

lo is the direct object pronoun for masculine singular (him / it).
So haberlo salvado is the textbook form.

However, in Spain there is common leísmo (using le as a direct object for a masculine person):

Agradezco haberle salvado.
Many speakers in Spain say this and consider it normal and natural.

So:

haberlo salvado → always correct and standard.
haberle salvado → very common in Spain for a male person; accepted by many as normal leísmo de persona.

Position: with an infinitive, the pronoun must attach to the end:

haberlo salvado, haberle salvado, salvarlo, salvarle
(not lo haber salvado).

Why isn’t there a de after agradezco? Could I say Agradezco de haber salvado…?

No, you shouldn’t say Agradezco de haber salvado… in standard Spanish.

Agradecer works like this:

Agradecer + noun/pronoun
- Agradezco tu ayuda. = I appreciate your help.
- Te agradezco el favor. = I thank you for the favor.
Agradecer + infinitive
- Agradezco haber salvado a mi hermano.
  I’m thankful to have saved my brother.
Agradecer que + subjunctive
- Agradezco que me ayudes.
  I’m thankful that you help me.

You do not insert de between agradezco and the infinitive here. Some verbs require de before an infinitive (e.g. tratar de, dejar de), but agradecer is not one of them.

Is Agradezco haber salvado a mi hermano del accidente different from Estoy agradecido por haber salvado a mi hermano del accidente?

They’re very close in meaning, but the structure is slightly different:

Agradezco haber salvado a mi hermano del accidente.
Verb agradezco = “I thank / I am grateful (for) …”
Estoy agradecido por haber salvado a mi hermano del accidente.
Adjective agradecido
- estar = “I am grateful for …”

Nuance:

Agradezco… can feel a bit more active, as if you are explicitly expressing thanks.
Estoy agradecido… sounds a bit more descriptive, like a state: “I am (in a state of being) grateful”.

Both are natural, and in everyday conversation they are often interchangeable.