Madrid has a complutense and an autonomous university. They have magnificent gardens around wonderfully modern buildings that are a good place to visit just for a slow walk around the grounds. There are four particularly important and popular libraries, out of the over one hundred, that house some of the biggest collections of books in Spain.
There are over two million books, manuscripts and forty six incredibly rare books. Some of the books in the collection are from all the way back to the 16th century. The Bibliotheca Municipal has around 120,000 reasonably rare books. The Ateneo library is smaller than other important Madrid libraries. The final important library is the Bibliotheca Real. It is on the ground floor of the Royal Palace museum which is picturesque and has lots of very unique and rare books that cannot be found anywhere else in Spain. The 250,000 volumes are found mainly in the form of manuscript and are among some of the oldest and rarest writings in the whole of Spain.
There are a large amount of art galleries and sculpture displays all over Madrid. The Direccion General de Patrimonio Artistico is considered to be the best in contemporary modern and classic artwork displays. You can get contact details for most of the up and coming artists in Madrid through any of these galleries, so you may be able to request a specific work at a reasonable price. The Centro de Arte Reina Sofia museum has on display the famous Gernica painting by Picasso.