Is Author House a legitimate publisher?
Author House approached me and wants to publish my novel. Are they a legitimate publisher and should I publish with them?
Publishing with Author House means that you will be self publishing your novel. They are a legitimate company, but they do not fall into the category of traditional publishing.
They are unlikely to care if your book is well written, but are in the business of selling services associated with printing and promoting books--of any quality.
You will have to pay to have your book designed, edited, produced, and promoted. You can buy services separately or as a package.
I've heard people refer to Author House as their "publisher," but in fact, they would be more accurate to refer to them as their "printer"--the printer who helped them self publish.
If you have worked hard on a book and it is ready for publication, I suggest that you first try to get an agent and sell the book to a traditional publisher, as they will pay you to produce and sell your book. You will not pay them.
For more on self publishing, see this Self Publishing article, and this companion article.