Hamburg never needed a king. For centuries it was a merchant republic that answered to its own senate, and you can still read that in the stone: the only palace in town is the town hall, the warehouses are red brick instead of gothic castle, and the harbor is the reason everything else exists. The city joined the Hanseatic League in 1241, and the full name is still the Free and Hanseatic City of Hamburg. It has also lost a lot: the Great Fire of 1842 took a third of the old town, and the bombing of July 1943 wrecked much of the rest. What you walk through now was rebuilt, twice, by people who wanted to keep trading.
It's Germany's second-largest city, with almost 1.9 million people, but it feels like a string of different places: the Alster lakes in the middle, the harbor and its warehouses to the south, St. Pauli's nightlife on the hill above the river, Altona and Blankenese along the Elbe. Between them run bridges, often counted at about 2,500. The weather is changeable, people say Moin at any hour of the day, and that's the whole welcome. Give it five days and it warms up.
This plan keeps each day in one part of the city: the brick warehouse district and the Elbphilharmonie, the old town and the memory of the bombing, the Elbe shore from a ferry to Blankenese, a train to Lübeck, and the Sunday fish market with St. Pauli and the Schanze. Day five has to land on a Sunday, so the plan assumes you start on a Wednesday (other starts are covered in the day 5 intro). Hamburg is also a good way into Germany as a whole: the port, the beer and the habit of understatement are very northern.