Learn Turkish: Sanayi geliştiğinden beri küresel kirlilik artıyor. - Since industry developed, global pollution is increasing.

It follows the pattern taught in this lesson. The verb gelişmek (to develop) takes the participle -dik, which changes to -tiğ due to consonant mutation and vowel harmony. Next comes the 3rd person possessive -i (referring to industry), the buffer letter -n-, and the ablative suffix -den (from). Followed by beri, it forms a phrase that literally means "from its having developed."

Why isn't it sanayinin geliştiğinden, since subordinate clauses usually pair the genitive and possessive?

You are right that these clauses normally use a genitive-possessive pair. However, when the subject is a general, non-specific concept (like industry in general, rather than one specific industry), the genitive suffix on the subject is often dropped. The verb part (geliştiğinden) still keeps its 3rd person possessive -i to hold the grammar together.

Is the word küresel (global) built from a smaller root word?

Yes, it is built from the noun küre, which means "sphere" or "globe". The suffix -sel (or -sal) is used to turn nouns into adjectives, similar to "-al" or "-ic" in English. So küre (globe) becomes küresel (global). You also see this in words like tarih (history) becoming tarihsel (historical).

Why does the main verb use the present continuous tense when it describes something that started in the past?