List the major trends in nineteenth-century architecture

What will be an ideal response?

Romantic architecture was perhaps a bit more staid when compared to the mediums of painting, sculpture, and music. Classical Greek and republican Roman buildings embodied the political and aesthetic ideals of nation builders like Napoleon and Jefferson and Neoclassicism was still used as a guiding architectural principle.
However, the austere dignity of the Neoclassical style did not appeal to everyone. The rise of nationalist sentiments gave rise to Neomedievalism (the revival of medieval culture), which exalted the state by recapturing its unique historical and cultural past. This style became known as Gothic and is perfectly captured in the British Houses of Parliament, whose picturesque combination of spires and towers was thought to express the dignity befitting the official architecture of a Christian nation.
As with the Transcendentalists, Romantic architecture also drew inspiration from the "exotic" East, and especially those parts of the world in which the European powers were building colonial empires. The Royal Pavilion at Brighton, for example, combines a fanciful assortment of Chinese, Indian, and Islamic motifs.