Se la vendistino proponus alian titolon, mi eble legus ĝin post kiam mi finos ĉi tiun ĉapitron.

Vendistino is made from several Esperanto pieces:

• vend- = the idea of selling
• -ist- = a person associated with an activity, often by profession
• -in- = female
• -o = noun ending

So:

• vendisto = seller, salesperson
• vendistino = female seller, saleswoman

This kind of word-building is very common in Esperanto.

La means the.

So la vendistino means a specific saleswoman, one already known from the context. If you said just vendistino, it would sound more like a saleswoman or any saleswoman, depending on context.

Esperanto uses la much like English uses the.

The ending -us is the Esperanto conditional mood. It is used for things that are imagined, hypothetical, or dependent on some condition.

So here:

• proponus = would offer
• legus = would read

The sentence is a hypothetical situation:

• Se ... proponus, mi ... legus
  = If ... offered / were to offer, I would read

This is a very common conditional pattern in Esperanto.

Yes. Esperanto and English do not handle this in exactly the same way.

In English, a hypothetical if-clause usually says:

• If she offered ...
• not normally If she would offer ...

But in Esperanto, using -us in both parts is normal for an unreal or imagined condition:

• Se ŝi proponus ..., mi legus ...

So even if English avoids would after if, Esperanto does not have to copy that pattern.

Because alian titolon is the direct object of proponus.

In Esperanto:

• direct objects usually take -n
• adjectives agree with the nouns they describe

So:

• alia titolo = another title
• alian titolon = another title as a direct object

Both words change:

• alia → alian
• titolo → titolon

That agreement is one of the most important patterns in Esperanto.

Alia means other, another, or different, depending on context.

So alian titolon can mean:

• another title
• a different title

It does not automatically mean new. For new, Esperanto would use nova.

Because ĝin is the direct-object form of ĝi.

• ĝi = it
• ĝin = it as the thing being acted on

Compare:

• Ĝi estas interesa. = It is interesting.
• Mi legus ĝin. = I would read it.

So the -n here works the same way as it does on nouns: it marks the direct object.

Eble means maybe or perhaps.

In this sentence, it softens the statement:

• mi eble legus ĝin = I might / would perhaps read it

Its position is somewhat flexible. You could also see:

• Eble mi legus ĝin
• Mi legus ĝin eble

But mi eble legus ĝin is very natural and clear.

Because post by itself is a preposition, and prepositions are followed by a noun phrase, not a full clause.

So:

• post ĉi tiu ĉapitro = after this chapter
• post kiam mi finos ĉi tiun ĉapitron = after I finish this chapter

Here, kiam introduces a clause with its own verb: mi finos.

So post kiam is the normal way to say after when a whole clause follows.

Because finos is talking about a future action, not a hypothetical one.

• finos = will finish
• finus = would finish

In this sentence, the finishing of the chapter is presented as a real future point:

• post kiam mi finos ĉi tiun ĉapitron = after I finish / after I will have finished this chapter

The hypothetical part is the offer-and-reading situation:

• Se la vendistino proponus ... , mi eble legus ...

So finos is appropriate because the speaker treats finishing the chapter as an expected future event, not as an imagined condition.

Because this phrase is the direct object of finos.

The basic form is:

• ĉi tiu ĉapitro = this chapter

But as a direct object, it becomes:

• ĉi tiun ĉapitron

Again, both the determiner-like word and the noun show agreement:

• tiu → tiun
• ĉapitro → ĉapitron

Also, ĉi tiu is the normal Esperanto way to say this.

In Esperanto, tiu means that / that one, and adding ĉi makes it mean this / this one.

So:

• tiu ĉapitro = that chapter
• ĉi tiu ĉapitro = this chapter

You can also place ĉi after the word:

• tiu ĉi ĉapitro

Both are correct, though ĉi tiu is often the form learners see first.