This lesson focuses on one particular conditional type known as the 'future unreal' which we use to talk about imaginary future situations. In plain English this is the words 'should, could, would'; I would go if I had time, I should call him tomorrow, I could talk to him.
We already have the basic conditional word Pi = If, so this is for more complicated sentences.
This is an idea I had whilst thinking about the King's Letter, the longest Sindarin text, particularly the line
i sennui Panthael estathar aen = 'who ought to be called Fullwise'.

Now, if we analyse this sentence, we see we have
i = the relative pronoun, 'who'
sennui = instead/rather
Panthael = 'Fullwise'
estathar = 'will be called'

And then we have aen at the end, which to my mind can only be to signify the conditional tense, changing estathar - 'will be called' into estathar aen - 'should be called'.

As you may be aware aen is one of the most controversial words in Sindarin. Every scholar has their own thoughts on what it means, and some prefer not to use it at all.

Usage

As the only example we have is for the future tense, I will not try and extrapolate it into other tenses.
In the King's Letter, aen is shown to follow the verb, so here are some examples that follow in the same vein:

Madathon aen = I should eat
Cenathol aen = You should see
Istatha aen = He should know
Tolathon aen na i mar gîn = I should come to your house
Aníratham aen lembas = We should want lembas