The Hofburg in Vienna shows many different architectural styles, from Gothic to Renaissance, Baroque to Rococo, and a smattering of Classicism and is in many ways a "city-within-a-city," comprising 18 groups of buildings, 19 courtyards, and 2,600 rooms.
Wien Hofburg Neue Burg Heldenplatz
The area around the Hofburg, along with some of its outlying buildings, houses a number of other attractions, including the Imperial Chapel (Burgkapelle), the Natural History Museum (Naturhistorisches Museum), the Austrian National Library, and the Spanish Riding School.
Hofburg, Kunsthistorisches Museum (English: "Museum of Art History")
The oldest continually used part of the Hofburg Palace, the Schweizerhof, was built in the early Sixteenth century and is where you’ll find the gothic Bergkapelle and the Royal Treasury; the Schatzkammer.
Hofburg Vienna, Schweizerhof
The Imperial Library, at first a standalone building, is one of the most vital parts of the Hofburg Palace for its creative value.
Hofburg in Vienna, the Austrian National Library
Text source: www.planetware.com and my own.