No cover. The tears and stains of concern are as shown in the photos. From a layman's perspective, it seems to be fine for reading enjoyment. Please also check the profile before purchasing. I am also selling many other picture books. I have done a simple check for page writing and underlining, but I have not completely checked all pages. Please forgive any minor oversights. As there are individual differences, please refrain from purchasing if you are sensitive. Please understand that this is a used item and purchase accordingly. For those who understand that this is a used item stored by a private individual, thank you very much.