I am an undergraduate student and I started looking for summer research opportunities. There are no opportunities at my own university and only a single REU (one of the most selective ones in the country, no hope of getting in) on the topic I am interested in. That's why I thought I might ask professors at a neighboring university about opportunities. Money is not an issue because I can get a grant from my own university. But I am not sure how to approach professors at another university. I audited a graduate class at said university this past semester. I cannot claim that I have a particularly close relationship with the professor, but I did talk to him a couple of times. Since this is the only professor I know, I was going to talk to him about opportunities at his university. His area of interest is the general area I am looking for, but I am not interested in the twist of his work. (Well, it's actually not that I am not interested. I am just so weak in the prerequisites for his approach that I doubt I could be productive or even just work semi-independently without someone holding my hand 24/7.) I am not sure about the best way to approach this conversation. Can I ask him for suggestions for other professors I might talk to, or would it be offensive if I did not ask him about a position first? Would it be more polite if I asked him first, and then asked about other professors only in case he declines? Or should I bypass him completely and talk to other professors directly? I do not want to offend him and close doors unnecessarily. On the other hand, I feel awkward just e-mailing professors at another university out of the blue. I will probably have to contact this professor (or others) via e-mail during winter break. The deadline to apply for an off-campus grant is two weeks after the break, so I should probably start getting in touch with professors before I get back to campus. I would appreciate your thoughts and suggestions!