So I have reached the point in my course where we are talking about the conditional verb form. In this particular course it is only touched on very briefly. I don't think it's really trying to teach it, so much as just make the learner aware that it exists by providing a few examples. Therefore, I am trying to supplement the course with the grammar guide here on Lernu.

If I understand correctly, the -US ending is used, when a state of being is imagined, i.e. If something were true, then something else would be true.

That seems simple enough. For instance, if I'm understanding it correctly, then these sentences would be correct:

Se mi havus filmon, mi spektus ĝin.

Se mi estus bona ŝaka ludanto, mi enirus la ŝakan turniron.

Mi manĝus la kuiradon de mia edzino, se ŝi estus bona kuiristo.

Are those correct? I hope so.

That seems to be the simple use of -US. However, according to the grammar guide here, it can also be used to state a "mild request or desire." In this case, in the examples presented, it's always presented as a polite request.

For instance, it seems that these sentences should be correct:

Ĉu vi transdonus la libron al mi?

Ĉu vi bonvolus malaltigi la muzikon?

Am I getting this or am I going wrong somewhere?

Comhghairdeas! You got it completely right.

Those "mild requests or desires" are just hidden conditionals:

Ĉu vi transdonus la libron al mi (se mi kuraĝus demandi)?

Ĉu vi bonvolus malaltigi la muzikon (se tio ne ĉagrenus vin)?

The best thing about -us is that it is tenseless. It works for the present, past and future!

Se vi donus al mi ovon hodiaŭ, mi redonus al vi kokidon morgaŭ.
If you gave me an egg today, I would give you a chick tomorrow.

Se vi donus al mi ovon hieraŭ, mi redonus al vi kokidon hodiaŭ.
If you had given me an egg yesterday, I would give you a chick today.

Se vi donus al mi ovon antaŭhieraŭ, mi redonus al vi kokidon hieraŭ.
If you had given me an egg the day before yesterday, I would have given you a chick yesterday.

So basically, any sentence of the types "if X did, Y would do" and also "if X had done, Y would have done" (and any mixture of them) simply translates to "se X farus, Y farus". It cannot get any neater.

Jes, ankaŭ mi gratulas vin.

There are two important things to remember about the imaga aŭ us-modo.
 

• It is really timeless, as Nornen already pointed out. While you may see different kinds of more or less convoluted expressions to express past tense, these are in most cases not needed and sometimes even wrong.
  
• The imaginary aspect as you yourself said. This is especially important when your English-language-ear would say "should", "ought" or "might". Stop and think, if it is really an imaginary situation or just something that needs to happen.

Eta parentezo:

PrimeMinisterK, Bonvolu ŝanĝi la lingvon de la fadeno. — Do jene
Esperanto → English

nornen:Comhghairdeas!

I mean, exactly!

nornen:You got it completely right.

Wow. Excellent. And just when I started to think I wasn't actually learning anything.

nornen:Those "mild requests or desires" are just hidden conditionals:

Ĉu vi transdonus la libron al mi (se mi kuraĝus demandi)?

Ĉu vi bonvolus malaltigi la muzikon (se tio ne ĉagrenus vin)?

The best thing about -us is that it is tenseless. It works for the present, past and future!

Se vi donus al mi ovon hodiaŭ, mi redonus al vi kokidon morgaŭ.
If you gave me an egg today, I would give you a chick tomorrow.

Se vi donus al mi ovon hieraŭ, mi redonus al vi kokidon hodiaŭ.
If you had given me an egg yesterday, I would give you a chick today.

Se vi donus al mi ovon antaŭhieraŭ, mi redonus al vi kokidon hieraŭ.
If you had given me an egg the day before yesterday, I would have given you a chick yesterday.

So basically, any sentence of the types "if X did, Y would do" and also "if X had done, Y would have done" (and any mixture of them) simply translates to "se X farus, Y farus". It cannot get any neater.

That's interesting. Thanks for the explanation. I will have to further ponder that. That's an interesting thought about them being "hidden conditionals."

I have to wonder then, in cases like that, is using the conditional mode required or just an option? For instance, instead of:

Ĉu vi transdonus la libron al mi?

Could you also just say:

Ĉu vi transdonas la libron al mi?

Or is that incorrect? I don't know. I guess actually the second one means, "Are you giving the book to me?" instead of "Will you give the book to me?" Is that right?

If that's right, then could you instead say:

Bonvolu transdoni la libron al mi. and essentially mean the same as Ĉu vi transdonus la libron al mi? Right?

Urho:Eta parentezo:

PrimeMinisterK, Bonvolu ŝanĝi la lingvon de la fadeno. — Do jene
Esperanto → English

Perdonu pri tio. Mi riparis ĝin.

(Did I use "perdonu" correctly there?)

Metsis:Jes, ankaŭ mi gratulas vin.

Well thank you. These last few days I really have felt like I have been spinning my wheels and doing a lot of work without actually increasing my understanding, so it's good to feel like I actually made some progress.

The first few days of learning Esperanto make things seem like they're going to go more smoothly than they actually do after you get past the simple stuff and really get into the weeds of more advanced concepts.

Metsis:There are two important things to remember about the imaga aŭ us-modo.
 

• It is really timeless, as Nornen already pointed out. While you may see different kinds of more or less convoluted expressions to express past tense, these are in most cases not needed and sometimes even wrong.

Can you provide an example of this?

Metsis: The imaginary aspect as you yourself said. This is especially important when your English-language-ear would say "should", "ought" or "might". Stop and think, if it is really an imaginary situation or just something that needs to happen.[/list]

In the case of "should" or "ought" would you use "bezoni"? What about "might"?

PrimeMinisterK:

Urho:Eta parentezo:

PrimeMinisterK, Bonvolu ŝanĝi la lingvon de la fadeno. — Do jene
Esperanto → English

Perdonu pri tio. Mi riparis ĝin.

(Did I use "perdonu" correctly there?)

Dankon! — Tamen eta korekto:
Perdonu pri tio. → Pardonu [al mi] pro tio.

Pardonu al mi, ke…

When Metsis refers to convoluted expressions, he probably has in mind such as below. Though why he thinks these are convoluted, I have no idea.

Vi povintus diri al mi, (vi estus povinta diri al mi) - you could have told me (trafoj en Tekstaro and here)

Mi konscias nun ke, mi devus esti restinta., se tiutempe mi ne vidis kialon por tio - I realise now that I should have stayed.

.... kvazaŭ ŝi estus mortonta - as if she were about to die.

That's interesting. Thanks for the explanation. I will have to further ponder that. That's an interesting thought about them being "hidden conditionals."

You are right to hesitate. It's somewhat forced to say, for example, that kion vi ŝatus trinki? or ĉu vi volus danci are 'hidden conditionals'

PrimeMinisterK,

This is an advanced topic, with which you should have waited for later.

Sudanglo pravas pri tiuj esprimoj, kiujn mi pensas.

Let's take an example: "I hadn't done the error, if you had told me the truth". If you use la imaga modo to translate that into Esperanto, then the Esperanto sentence means that I made an error because you didn't tell me. There are (at least) three ways to express (1) the time and (2) the imaginarity.
 

• erroneous: Mi ne farintus la eraron, se vi dirintus al mi la veron
  
• too complex: Mi ne estus farinta la eraron, se vi estus dirinta al mi la veron.
  
• best: Mi ne farus la eraron, se vi antaŭe dirus al mi la veron.

Furthermore such forms as devintus, povintus for "should" and "could" are outright wrong.