Adobe Reader is all you need if you just want to write reminders to yourself on a PDF. But if you want to work collaboratively with other students, each of you annotating the file and commenting on each other’s comments, or if you want to be able to search your notes from outside the file with a view to locating it again, you’ll need something more sophisticated.
Search your notes
The search facility included in PDF-XChange Editor (free download) allows you to search the annotations in a file or a folder of files. It also has a full set of features for annotation. It's Windows only, but there's an alternative for Mac users in the form of Skim (free download). When you annotate a PDF in Skim it makes those annotations available to Spotlight, the built-in file indexer in OS X. So you can then search in the Finder for a term in your notes and the appropriate PDF should be found.
ReadCube is a free service with extensive annotation tools and a very clever trick of transforming references in an article into live links to the articles referred to. You can search your notes but can’t collaborate with others. The notes you make aren’t compatible with Adobe Reader so you should be sure that you like the service before committing to it with lots of notes. Reviews of ReadCube suggest that it's most useful in the fields of life sciences and medicine and perhaps has less to offer to humanities students.
There are many options for students who want to collaborate. However, the annotation systems use different methods to store the notes so not all annotations can be shared via all systems.
A.nnotate offers extensive online annotation tools and easy sharing. The free account offers 30Mb of storage, file sharing and in-document collaborationfor up to 3 users each month but the paid accounts are reasonably priced if you need more. Both document and annotation are indexed and searchable. There are no limits on the number of times a document may be shared or on the number of people sharing.
Mendeley is a referencing tool and academic social network that allows you to annotate and share pdfs. Free accounts are available but it won’t work successfully unless all members of your collaborating group are also members of Mendeley. However, the referencing and citation facilities may be attractive to everyone over and above the collaboration, and it’s free to join.