There are two things that are challenging about learning to run. First is just the straight fitness aspect, and the second is your body having to adjust to the impact.
Obviously, going uphill is harder work from the cardio perspective, but this generally speaking shouldn't pose a safety issue.
The impact issue is the one that really takes time for your body to adjust, and is where potential injuries occur, from trying to do too much, too soon. But going uphill is actually easier from an impact perspective - you are likely going slower and taking smaller steps, which means less impact. Also, the slope means you are hitting the ground slightly earlier in your stride, which also means less impact. I agree with Coral - where you need to take care is going downhill - keep your speed down, and take smaller steps here also.
The reasonable man adapts himself to the world; the unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man.
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