Although you must respect the basic safety rules that you already follow at home, you'll have nothing to worry about during your trip to Norway, because the country is very safe.
During your trip to Norway, you'll quickly notice that you have set foot in a very safe country where safety problems are quite unusual. Be aware that this doesn't mean that you can stroll around without respecting any obvious rules for safety, but in the end you don't need to do any more or less than what you do in your everyday life. Norway may be a very safe country, but like everywhere else in the world, there are some people who are more dishonest than others.
In big cities, on public transport or in more touristy locations, you may encounter pickpockets. Cases of assault are very unusual.
If you get the idea to buy any hard or soft drugs, however, you should know that you'll be dealing directly with a disreputable population.
As for everything else, there isn't much to complain about, but just know that while travelling the roads, you'll encounter a great many herds of sheep and moose. Also know that during your hikes, the weather can change often and fast.
Apart from respecting the obvious and basic safety rules that already dictate your everyday life, there isn't much else you have to do. Just avoid drawing too much attention to yourself. Don't show any pretentious display of wealth. Keep an eye on your belongings, and always be a little more attentive in tourist areas and on public transport.
If you are assaulted, the rule is the same as everywhere else in the world, don't resist. Stay as calm as possible and just give them what they want. It is important to never keep all your money in one place, have several hiding places and keep an amount on hand that may be enough to satisfy your attacker.
On the road, simply be careful and adjust your speed to the roads and to weather conditions. These rules should systematically be observed before and during all hikes.