First iI'd like to adexpress how cool it would be to be able to go back in time.

From a stylistic perspective, you can omit this sentence entirely. It's not necessary to tell the audience that you're going to describe how cool something is--simply start describing it in a cool and interesting way (which you do in the next sentence)

Especially for me, someone who is really interested in gGerman history (as well as history in general), being able to go back in time would be quite the dream.

Given that i know that i'm aProvided I know I can time traveller, of course ;).

First and foremost i would love toI would visit the time aroundperiod between 1880 to around 1890.

First of all, iI'd love to see my hometown back during this time.

You used "first" already in the previous sentence. Avoid using "first" again to avoid confusing the reader on the actual sequence.

I probably wouldn't even be able to recognize it but it would be interesting to see how the city evolved and became biggergrew over time.

Also, this time isI generally afind this time i finperiod interesting.

In general, use "time" to describe a specific point in time, and "time period" to describe an approximate range (at this scale)

Therefore it would not just be an adventure but also a way to educate myself further: i--I strongly believe that reading about a certain time in an history book is not comparable to actually living in it.

":" are generally used for a list of items, whereas "-" or "--" are used to connect ideas.

The feeling, the atmosphaere, the people: --those are things a book can certainly describe but it'll never come any close to equalizingdescribe. But reading books about a place can never match the experience of having actually lived there.

Regarding the time, it was a time of upcomimpending socialist- movements in Germany (especially in the form of the SPD, a workers party that emerged and later got banned and persecuted) and startingearly industrialization (hence the uprising of more workers' parties).

"impending" is more accurate when talking about the past from the perspective of the present--i.e. when we know what's going to happen next. "upcoming" is more appropriate when it hasn't happened yet.

But also the conflict with the church could be interesting to observeinteresting to observe could be the conflict with the church.

The Kaiserreich is also a time militarism of the era, something that iI haven't had the experience to observe yetd in my own life and time (quite lucky actually!).

I would also want to see how rural life would changeas different, especially for peaseants.

"would change" suggests you are observing the change between 1880 and 1890. Whereas I think you mean comparing what you see in your time travels and what you observed in present time, for which "was different" is better suited to point at the act of comparing. One is a comparison and one is a series of observations, so different word choice is called for.

I also would love to see my city evolve and visit the place i'mexact place where I'm currently writing this from.

Modified for clarity (yours was fine too)