In order for us to help you better, give us more detail.
What specifically is making you feel safety is an issue? Have you had any actual bad experiences with safety? (If someone has actually been mugged, saying "don't worry about mugging" is not too helpful). Or, is this based on something you've read or seen on TV? Is this based on general fear of big cities? Or is it based on fear of the unknown, since it's your first trip to Europe?
Where do you live and work, so what kind of place are you used to on a regular basis? (I agree with Pam that it's easy to say "take the standard big city precautions," but that only helps if you know what they are, and are so used to them that don't have to think about them too much).
What's the largest city you've visited? How comfortable did you feel there?
Are you planning "nightlife" such as bars and clubs? These can definitely have safety issues (anywhere in the world) that are not present when visiting, say, museums and restaurants.