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As like many areas in Scotland, safety should not be a huge concern for travelers. Glasgow is the only city in Scotland that has a problem with violent crime. Inverness, however - it's more quaint countryside - violent crime is not a big issue in these parts. You may want to skip wearing the English football jerseys just to avoid harassment from any local youths who might not hold a favorable opinion of the Queen's teams (think Yankees fans in Red Sox Nation, or vice versa), but that's about it.
Otherwise, normal common sense applies. Be aware of your surroundings, don't walk alone at night in unfamiliar areas and keep an eye on your belongings. With so many opportunities for hiking and walking, just make sure someone knows you've gone if you decide to go alone. Be careful if you're drinking in the pubs alone - while most locals are nothing but friendly, you never know if someone has alterior motives (particularly with the single woman travelers).