Regarding copyright on a book:
a) If you’re trying to get an agent, DON’T PUT THE COPYRIGHT SYMBOL OR THE WORD COPYRIGHT ON YOUR TITLE PAGE. It makes you look like an amateur, because
b) You automatically own the copyright to your work as soon as you put it in a fixed form. You do not have to announce that it is yours for it to really be yours.
c) Also? Nobody wants to steal your ideas. It is very hard to execute an idea, and a lazy person would not be up for the task of making a good book out of your idea and trying to sell it. If you’re really worried that literary agents are out to reject your book but secretly sell it for themselves, you are a conspiracy theorist.
d) Yes, theft occasionally happens. Generally not at that level and not by agents, though. But if it is going to happen, slapping “copyright” on your work is not going to stop it.
e) Registered copyrights exist so you can pay money to prove via an outside source that the copyright belongs to you. You have a copyright even if you don’t register it, but you should not register a copyright for a book in your name if you are trying to sell it to a publisher. They will copyright the book.
f) If you really are truly unable to stop worrying that someone is going to swipe your idea because it’s just that good (even though an agent is hoping to collect part of your paycheck for selling it for you), buy some peace of mind by sending the manuscript to yourself through the mail in a sealed envelope so you can prove, due to the postage stamp date, that it has been yours since at least that date. (The process is affectionately called “the poor man’s copyright.”) This doesn’t necessarily hold up in court, but at least it’s evidence of some sort that you wrote this thing and put it in a package that’s been sealed at least X long.
g) I don’t mean to shame anyone for worrying that your precious hard work might be taken from you, but ideas are cheap and selling them/fleshing them out is hard. Agents, especially, are in a business that helps connect writers to publishing opportunities. They want you to write the book and succeed. They have nothing to gain as an agent by sneaking off with your work, and if you’ve done your research on agents, you should know which ones are reputable. Don’t submit to anyone disreputable and you’ll be fine.