Above all, Strasbourg is known for being the headquarters of the European Parliament, along with Brussels and the general secretary office is located in Luxembourg. Strasbourg is one of the few cities that houses an international institution without being the capital of the state (along with Geneva and New York, I believe).
The European Parliament is one of the world's most powerful legislators and it represents the European population. It's one of the EU's main legislative institutions, along with the European Council. It's the only European institution chosen directly by the citizens of the EU. It's elected by universal, direct and secret suffrage every 5 years.
Its main purposes are: to debate and approve the legislation of the EU, to control the EU's other institutions in order to guarantee that they are functioning proper and to debate and adopt the EU's budget (it shares the first and third purpose with the European Council).
The number of MEPs is proportional to the population of the EU, although it can't be a number greater than 750 - 751 over all, if we take the president into account (the president is currently Martin Schulz). They are grouped together by political similarities. It has nothing to do with nationality.
The Hemicycle is one of the most famous rooms, with a capacity of 750 people. They hold monthly sessions in this room. I entered it in a guided visited and they explained several things to us (although the visit was in French and as it was at the beginning of my stay, I barely understood anything).
They finished constructing the building in 1998. It's very pretty and impressive - as much so on the inside, as on the outside so it's worth visiting. On one hand, it's surrounded by water so the views are really good. In fact, I also went to the European Parliament in Brussels and there was no point of comparison in terms of the views and construction of the building. What's more, if it's seen from above or one of the sides, it resembles the prow of a boat which is going to start sailing. It's made of glass, metal, sandstone and wood. Inside it, there are some areas in the open air with plants and of course, there are many flags. No one could ever be left indifferent to the building's dimension and design. It's over 200, 000 metres cubed and includes 1, 133 offices, 18 commission rooms and the Hemicycle, of which I previously spoke about.
Regarding the visits inside the building, they are usually in groups and booked in advance. I was lucky to go with the 'Strasbourg aime ses étudiants' association for free (although I think all the visits are free). There are various visits organised with this organisation to this institution, as well as to others close to the Parliament (Human Rights, etc. ). They also organise visits with my university and I believe you can reserve it on your own behalf. If you don't go inside, it's at least worth visiting it for the exterior. At the end of our visit, they gave us free posters of the views of the Parliament, both in the day and at night. Inside, it's very spacious and light with a new and modern appearance, although I'm left with the view of the building with the surrounding river. I liked the circular entrance out in the open air a lot too. I was the first thing I saw and a ball shaped monument right in the centre really caught my attention. You could see people of all class and culture there.
Another curious piece of information is that in the surroundings, there are several campaign tents, with posters demonstrating something. At first it shocked me quite a bit. They also camped right on the river border and the city is somewhat cold but later, I became conscious the importance of this institution, thanks to the famous cases they broadcast on the news. I suppose there isn't a better way of protesting, than in front of the European Parliament.
You can get there by walking from the the Orangerie park and through Robertsau and also by bike, tram or bus. The tram stop is called 'Parlement Européen', it's line E in the direction, 'Robertsau Bocklin'. In Spring, (I don't know if they do it during the rest of the year) I was able to get to the Parliament for free, in a tourist boat with some friends and then it also brings you back to the boat station.