There is a sentence in Lingua Latina per se Illustrata Chap. 28 that I can't understand.
Lydia libellum, quem adhuc intra vestem occultavit, promit et Medo ostendit. Qui manum extendens libellum apprehendit et "Qui liber est iste?" inquit.
What is the first qui for?
I thought it should be a relative pronoun identical to Medo, but why is it capitalized in another sentence instead of in the previous one?
What is the verb for the main clause and what for the subordinate clause?
It should be remembered that this type of punctuation and capitalization is merely modern convention. In this paragraph, I imagine Orberg chose to capitalize the qui as a convenience of breaking up the sentences, so that they wouldn't be too unwieldy. It could easily have been written with a comma and a lower case q:
and shows it to Medus, who, extending...
The reason some editors (and presumably Orberg here) adopt this convention is that qui in Latin can also have the force of a conjunction + a relative, as Allen and Greenough mention here:
When the antecedent is in a different sentence, the relative is often equivalent to a demonstrative with a conjunction.
quae cum ita sint (= et cum ea ita sint) [and] since this is so
As you suspected, qui is a relative pronoun which refers to Medus. However, differently from English, in Latin it can sometimes show up in an independent clause, referring to something that preceded. In such cases, it can be translated with the appropriate pronoun:
Extending [his] hand, he took the little book...
This usage of the relative pronoun is described in Latin Grammar by Allen and Greenough:
f. A relative pronoun (or adverb) often stands at the beginning of an independent sentence or clause, serving to connect it with the sentence or clause that precedes.
