Hofburg “Castle of the Court”, was built in the 13th century, and is the former principal palace of the Habsburg dynasty in Austria.
Originally, it was planned to be used as the seat of the Dukes of Austria (976-1246), but as their power expanded over the centuries, so did the palace.  It served as the seat of the Habsburg kings and emperors of the Holy Roman Empire, and then the seat of the Emperor of Austria in 1918.  Today it is still used as the seat of the head of state, the Austrian Federal President.
 

Schönbrunn Palace was the main summer house and hunting lodge for generations of Habsburg rulers.
In 1569, Holy Roman Emperor Maximillian II (1564-1576) purchased a plot of land and ordered that it be used as the recreational hunting ground for the court.  It was fenced off and populated with game such as pheasants, ducks, deer, and boar.
On the land, was a 14th century mansion called the Katterburg.  For the next century, it was used as a hunting lodge, but more attention was focused on extending the grounds than the upkeep of the mansion.
Emperor Ferdinand II (1619-1637) and his wife Empress Elenora von Gonzaga were passionate hunters and would often throw hunting parties here.  After Ferdinand’s death in 1637, the estate become the dower residence to Empress Elenora, who needed the proper setting for her busy social life.  In 1642, she had a château de plaisance (literally translates to pleasure castle) built. It was then that name changed to Schönbrunn.
Forty years later, the château was desecrated by the Ottoman troops during the Seige of Vienna (1683). By 1686, the Palace was back in Habsburg possession, and remained so until their downfall in 1918.
With the newly founded Austrian Republic, the Schönbrunn Palace was preserved into a museum. The Palace has remained a museum since then, with the exception of being used as British office space during WW2.