The First Reich: The Holy Roman Empire (800/962 - 1806)
Although the name dates to the twelfth century reign of Frederick Barbarossa, the Holy Roman Empire was created over 300 years earlier. In 800 AD Charlemagne was crowned emperor of a territory which covered much of western and central Europe; this created an institution that would remain, in one form or another, for over a thousand years. The Empire was reinvigorated by Otto I in the tenth century, and his imperial coronation in 962 has also been used to define the start of both the Holy Roman Empire, and the First Reich. By this stage Charlemagne's empire had been divided, and the remainder was based around a set of core territories, occupying much the same area as modern Germany.
The geography, politics and strength of this empire continued to fluctuate massively over the next eight hundred years, but the imperial ideal, and the German heartland, remained. In 1806 the Empire was abolished by the then Emperor Francis II, partly as a response to the Napoleonic threat. Allowing for the difficulties in summarising the Holy Roman Empire - which parts of a fluid thousand year history do you select? - it was generally a loose confederation of many smaller, almost independent, territories, with little desire to vastly expand across Europe.
The Second Reich: The German Empire (1871 - 1918)
The dissolution of the Holy Roman Empire, combined with a growing feeling of German nationalism, led to repeated attempts at unifying the multitude of German territories, before a single state was created almost solely by the will of Otto von Bismarck. Between 1862 and 1871 this great Prussian politician used a combination of persuasion, strategy, skill and outright warfare to create a German Empire dominated by Prussia, and ruled by the Kaiser. This new state, the Kaiserreich, grew to dominate European politics at the close of the 19th, and start of the 20th, century. In 1918, after defeat in the Great War, a popular revolution forced the Kaiser into abdication and exile; a republic was then declared. The German Empire was the largely the opposite of the Holy Roman, despite having the Kaiser as a similar imperial figurehead: a centralised and authoritarian state which, after the dismissal of Bismarck in 1890, maintained an aggressive foreign policy.
The Third Reich: Nazi Germany (1933 - 1945)
In 1933, President Paul von Hindenburg appointed Adolf Hitler as Chancellor of the German State. Dictatorial powers and sweeping changes soon followed, as democracy disappeared and the country militarised. The Third Reich was to have been a vastly extended German Empire, expunged of minorities and lasting for a thousand years, but it was removed in 1945 by a combined force of allied nations, which included Britain, France, Russia and the US. The Nazi state proved to be dictatorial and expansionist, with goals of ethnic 'purity' that formed a stark contrast to the first reich's broad assortment of peoples and places.