PDF Files Manipulation Detection

There is an entire science behind this kind of thing, called forensic document analysis, but it's not a trivial task. You will need some advanced (and often expensive) tools to be able to detect such things. PDF files can contain a sort of "cache" of previous versions of themselves, or a record of revisions done to them, so in theory it's possible to detect that a file has been modified after its initial creation, but it depends on many factors.

Are you hoping to detect whether the file was modified BEFORE you got it? No hope of that at all, unless it was signed by someone else. 

You must apply a digital signature using a certificate you own. Acrobat can detect whether the file has been modified since you created it (because any change does not match the certificate).