The Austro-Hungarian Empire was also known as Austria-Hungary and the Dual Monarchy. In 1867, the Habsburg Empire (Austria) joined up with the Kingdom of Hungary and became the second largest empire in Europe after the Russian Empire. 
It was a pretty odd setup. The Habsburg monarch ruled Austria and the Hungarian king ruled Hungary. There were two capitals - Vienna (the main one) and Budapest. Austria and Hungary each maintained separate parliaments. There were no common laws between the two. Any proposed law had to pass both parliaments. There was no Austro-Hungarian passport. A person was either an Austrian citizen or a Hungarian citizen.
The empire was made up of many ethnic groups. The official languages were German, Hungarian, Czech, Polish, Ukrainian, Romanian, Croatian and Italian. The unofficial languages were Serbian, Slovak, Slovenian, Bosnian, Rusyn and Yiddish.
The territory took up most of Central Europe. Using today's map, it covered Austria, Hungary, Bosnia and Herzegovina, Croatia, Czech Republic, Slovakia, Slovenia, large portions of Serbia and Romania, and bits of Italy, Moldova, Montenegro, Poland and Ukraine.Following the assassination of the Archduke Franz Ferdinand in Sarajevo, the Austro-Hungarian Empire declared war on Serbia. Austro-Hungary was allied with Germany, Serbia was allied with Russia. Everyone else got pulled in due to various military alliances and we ended up with WWI.
At the end of WWI, in 1918, the Austro-Hungarian monarchy collapsed. It's amazing that Austria-Hungary even lasted for 51 years.
Update: I've received lots of feedback that the second map above isn't accurate. I didn't draw the map. Maybe this map will be better received.
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