There are a number of Periods or Styles of architecture.
While many ideas, forms and architects do not necessarily fall into classifiable zones, this is an attempt to organize the field systematically.
Roman architecture - Amphitheaters, basilicas, aqueducts, baths and temples constructed largely of stone, concrete and brick and featuring the development of the arch.
Composite - used Ionic scrollwork with Corinthian leaves;
Romanesque architecture (Norman) - Vaults and arches created from stone and buildings of thick stone characterize Romanesque architecture. Interiors simple and severe with geometric designs.
Byzantine architecture[?] - Dome characterized this period, plaster added to outside surfaces as a building medium. Interiors brightly colored and ornate, using marbles and mosaics for frescoes and decoration. Iconagraphy and Iconstasis walls a focus.
Gothic architecture - High naves with flying buttresses[?], bridges of stone and large windows sectioned into many small panes by stonework are features of this style. Pointed arches, elaborate carving, curved windows, and doors developed.
Renaissance architecture - Revival and adaptation of Greek and Roman architecture featuring domes and rectangular columns frequently embedded in walls.
Baroque architecture[?] - - Ornate style with elaborate carvings using gilt, plaster and paint in flowing curves and designs.
Rococo - A more ornate Baroque style featuring illusionism, a focus on the oval shape, interiors, and less of a stress on building materials.
Art nouveau - (or Eclectic and revival styles[?]) - An 1890s style in architecture, graphic arts, and interior design characterized by writhing forms, curving lines, and asymmetrical organization. Some critics regard the style as the first stage of modern architecture.
Chicago school - This movement is marked by utilitarian construction of factories, apartments, and railroad stations. Durability stressed in use of steel, iron, cement, and wrought iron, reinforced glassed used to create domed ceilings. In particular, they pioneered use of steel construction in high rise buildings. It is related to the Prairie school[?] of residential architecture.
Art Deco - A 1920s style characterized by setbacks, zigzag forms influenced by Egyptian art, and use of chrome and plastic ornamentation. New York' s Chrysler Building is an architectural example of the style.
International style[?] - (Modern Architecture)- Low steel constructed buildings with glass walls covering large areas in vogue at beginning, then evolved into glass box high rise. Bauhaus School[?] pioneered this style.
Note - any classification of style/subject/form/idea of the last 20-30 years is highly suspect as taboos, influences and human nature cloud the classification system.