If you are looking to buy non-Spanish books in Las Palmas, you have several options:
Libreria IDIOMàTIKA (Triana)
This bookstore is specialized in international books! They are located close to Triana at Calle Senador Castillo Olivares 52. IDIOMàtika sell books in dozens of languages and have an online catalogue.
Libreria IDIOMàTIKA (Las Canteras)
A small bookstore at Plazoletta de Farray, specialized in books in different languages.
Re-Read sells second hand books for a good price. 1 book for €3 / 3 books for €5 / 5 books for €10. They are located very close to Un Lugar at Calle Bernardo de la Torre 33.
El Rincón del Lector
This second hand bookstore is located in Vegueta, close to the cathedral, at Calle San Marcial 3. They have an online book catalogue which is updated regularly, so you can see if they have the book you want from the comfort of your own home.
El Corte Inglés
This popular department store at Av. José Mesa y López 13 also has a small section with international books. Make sure you go to the right building; books are sold at the ground floor at the El Corte Inglés building with Starbucks/Café Regina/Gourmet Store.
BookCrossing at El Muelle
The concept is easy; bring a book -> take a book! They have books in different languages available and are located at the Centro Commercial El Muelle.
Librería Canaima at Calle Senador Castillo Olivares 7 (close to San Telmo) is a big library with lots of books. They sell English studybooks to learn Spanish. I am not 100% if they also sell international books, but they can order books for you.
Share your experiences and recommendations in the comments!