Ossolineum is a beautiful Baroque palace, built between 1675 and 1715, that once housed the Jesuit school, part of the Leopoldine University. Today, this red building on the Odra hosts the National Library, founded by Count Ossoliński in L'viv.
You should not miss it! I think it is one of the most beautiful buildings apart from those of the Rynek.
The Ossolineum Institute hosts one of the largest scientific libraries in Poland, special interest being laid on Polish and Slavonic history, culture and literature, a publishing company and a museum/gallery. It origins in Lemberg/Lwow and was transferred after 1945 to Wroclaw - unfortunately not completely; the larger part of the collections is still in the Ukraine.
The institute was founded by Józef Maksymilian Ossolinski (1748-1826), a writer, collector and scholar in Lemberg/Lwow in 1817 when he handed over to the Polish nation valuable collections of books, manuscripts and museum pieces.
As a tourist you're not entitled to use the library or see the main reading room - you need to subscribe to the library for that. However, sometimes (like when I visited) there are exhibits in the Ossolineum which you can see. I was so lucky to see a small but very nice exhibit (free) of Dürer and Rembrandt drawings/prints contrasted with modern pieces of Polish artists. But even if there are no exhibits then don't hesitate to enter the building and see the two quiet courtyards (see pictures) and admire the beautiful 17th century Baroque architecture (originally a hospital) after plans of Jean Baptiste Mathey from Burgundy.