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Berlin is a relatively safe place. The public transport system works very well, mostly throughout the night and everyone uses it around the clock. So even at nighttime there is generally no problem in getting home safely. But of course there is criminality and you have to be aware of it. Especially in touristic areas there are a lot of pickpockets. In clubs there are sometimes drug dealers present, but they will leave you alone if you show no interest.
You should avoid parks at night. You never know who is creeping through the bushes. Some areas in Kreuzberg, Neukölln and Friedrichshain can get rough at night, so try to avoid trouble by being vigilant. At night Berlin is a party town and especially young people from around the world dive into the vibrant nightlife. As everywhere mind your safety.