Will literary agents consider taking a look at work like this: A manuscript of collected short stories. All having something to do with each other of course. Or do L.A.'s tend to not want to deal short story collections? Thanks. I hope this question doesn't sound stupid.

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Short story collections are typically saved for either non-fiction themed collections, like Chicken Soup for the Soul, or fictional stories written by well-known authors. Short story collections are much rarer for unknown writers to publish. You'll have a much better chance of publishing your short stories one at a time in literary magazines.

This problem with short story collections, much like poetry, is that it doesn't sell. Unless you're an established author of novels, or you've been able to get your name out there by getting your stories published in mags then it'll be extremely hard to get a collection published as an unknown writer. Literary agents aren't signing up clients who ONLY have short stories because publishers aren't buying them from new, unknown writers. And, publishers aren't buying them because the reading public aren't buying them. duotrope.com has a list of mags. Only the paying ones, mostly the professional paying ones, are worth a publishing credit. ADDING: Oh, I forgot to say that this is for physical books. Ebooks might be different so you might want to look into some royalty paying ebook publishers. You wouldn't need an agent for this + many ebook publishers don't pay advance, so it wouldn't be worth it to an agent to represent for ebook only, either, unless it was maybe ebook for their current client or ebook-only imprint from a major publisher.

It's very difficult to sell short story collections. You didn't say what genre your stories are. Some westerns are picked up, as action and thrillers. There are several mystery anthologies also. This author has several short story collections. http://www15.brnkster.com/jur1/index.html