As we are limited in space, below is a few ideas to help get you started and understand the architecture a bit better:
The Harold Washington Library in Chicago was designed in 1987 by the architectural firm Hammond, Beeby, and Babka, and the ornamentation on the roof was added in 1993. The exterior of the building was particularly influenced by other Chicago landmarks, such as the Rookery. Just like the Rookery, built in 1888, the library's exterior is made up of mostly red brick with decorative ornamentation. Even the library's interior winter garden on the 9th floor is modeled after the Rookery's light court, which is covered with an all glass, aluminum, and steel ceiling. The most notable fact concerning the design is that it is a mix of both late 19th century design and contemporary design.
The building's exterior can be linked to having been inspired by the Beaux-Arts architecture movement that began in Paris in 1671 but heavily inspired American architecture in the late 1800s to the early 1920s. The Beaux-Arts style particularly reflected neoclassicism and made use of Baroque and Rococo ornamentation. We especially see neoclassical ornamentation presented on the library's glass roof. The acroteria, meaning architectural ornaments mounted on a flat base, seen on the roof are owls, which are the symbol of knowledge and very fitting for a library, and seed pods to represent Chicago's agricultural heritage. There are also wall medallions of the face of Ceres, the Roman goddess of grain, and ears of corn, both of which also symbolize Chicago's agricultural ties. The ornamentation was designed by Kent Bloom in 1993.
However, while the exterior of the building reflects neoclassical and Beaux-Arts design, the interior is very modern. The modern interior design is especially seen in the glass, aluminum, and steel ceiling that houses the winter garden and a restaurant, and, as already stated, the ceiling of the winter garden was modeled after the light court in the Rookery building.
Hence, the relationship between the interior and exterior of the building is that the exterior reflects Chicago's older, historic culture, while the interior reflects Chicago's modern culture, and the two design strategies serve to unite Chicago's past with its present.