The evince package which is built-in in Ubuntu and is called Document Viewer can add annotations to PDFs. Starting with Ubuntu 15.04, Document Viewer can also remove annotations. Evince 3.18.2 from the Ubuntu 16.04 default repositories has support for adding highlight annotations, as well as squiggly highlight annotations and moving text annotations.
If you do not have a visible side pane on the left side of the opened document's window, click View -> Side Pane or press F9 to make the side pane visible. At the top of this side pane, there is a dropdown menu with options like Thumbnails, Index and Annotations (some of which may be dimmed for some documents).
To create an annotation:
Select Annotations from the dropdown menu. You should now see List and Add tabs under the dropdown menu.

Select the Add tab.
Click on the icon to add a text annotation.
Click on the spot in the document window you would like to add the annotation to, preferably a blank spot where the annotation will not cover anything else in the document. Your annotation window will open.
Type your text into the annotation window. You can resize the note by clicking and holding the left mouse button on one of the bottom corners of the note, and moving it around.
Close the note by clicking on the x in the top corner of the note. You might need to hover over the x with the mouse to make it visible.