View your own profile, button in bottom right with your portrait, also P key, when in mansion. Lists your reputation, and mage order rank.
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Take and complete custom requests in slave traders. Explore outskirts and save people being harassed by bandits. Make sure you release the captured people. Also works from bandit camps, or any other time it mentions "other people involved", if you release them after the fight then you gain reputation. Sometimes (or very frequently in current version because of bug), they give you a choice of options to repay you, if you refuse, you get more reputation. Though personally, I tend to ask for monetary as sometimes that gives items with extra stats.