An excellent resource for advanced students is John D. Murphy's Azerbaijani Newspaper Reader (Kensington, Dunwoody Press). This book contains 25 selections from Azerbaijani newspapers from the early 1990s along with a brief overview of Azeri grammar. Each selection is translated at the end of the book and also includes helpful grammar notes for difficult constructions and translations of idiomatic expressions.
The first edition (1993) uses the Azeri Cyrillic alphabet while the subsequent edition (1997) uses the Latin alphabet. I managed to get a photocopy of the 1993 edition and found it very helpful to get accustomed to the Cyrillic alphabet. Not only is a knowledge of Cyrillic crucial for all Soviet-era historical research, many older and even many younger Azeris feel more comfortable reading and writing in this alphabet.
However, I found that transliterating the Cyrillic text into Latin sped up my translations. I am posting the transliterated texts here for other students who may have access to the Cyrillic edition but who are not interested in learning the Cyrillic alphabet.