I learned about the PDF possibility of taking notes which are then stored with the document, usefull when reading ebooks. If the note taker also supports some math notation, that would be wonderful! Which free PDF reader can do this? (I am using Lubuntu 12.10)
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1possible duplicate of How can I highlight or annotate PDFs? – landroni Jan 24 '15 at 18:46
11 Answers
I suggest you try these two programs and choose the one that better fits your needs.
Xournal
sudo apt-get install xournal
All annotations are hand made (so to speak). You can print them on the PDF, if you want, or you can set them apart.
Mendeley
Download from here. Very useful to keep track of your research notes.

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4Xournal doesn't save annotation in the pdf file itself, so if you send the file to someone else, he won't get the annotations. – To Do Jun 01 '13 at 10:38
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14You must "Export to PDF" to generate a new PDF with the annotations. This way anybody can read them. – Ed Villegas Jun 02 '13 at 13:40
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How can you save your annotations directly to PDF using Mendeley? – Georgy Ivanov Nov 21 '13 at 14:02
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1Yes, you can. Just go to «Export to PDF with annotations» in the «File» menu. – Ed Villegas Nov 24 '13 at 18:03
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xournal sucks regardless, because it just shows the pdf as a canvas and the links and interactive elements don't work. – Mark Jeronimus Nov 24 '21 at 19:45
Evince 3.6.1 (the default PDF viewer) now supports adding annotations and bookmarks (proper PDF bookmarks), that are saved with the document.
Since Evince 3.14 you can add and delete annotations.
UPDATE Evince 3.14: Annotations can be added and deleted.
UPDATE 2020: Key S
adds a text note and Ctrl + H
highlights selected text. (both still require a mouse click to start writing on the annotation). Thanks @Gogowitsch

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3Maybe I just do not see it, but I can't move or delete annotations in evince. I'm using the ubuntu 13.10 default version (3.10). – verpfeilt Oct 19 '13 at 23:02
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3yup, that is a pending feature https://help.gnome.org/users/evince/stable/annotations-delete.html.en – alfC Oct 20 '13 at 19:50
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4With GNOME 3.14, removing annotations has been finally implemented. See https://wiki.gnome.org/ThreePointThirteen/ReleaseNotes (evince: supports removing annotations). – Peque Dec 10 '14 at 22:13
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2If you're looking for it and can't find it, in Ubuntu, Evince is called Document Viewer. – Brad Turek Sep 24 '18 at 15:44
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1Look at the keyboard shortcuts to work with comments efficiently. For instance, the key S adds a note. – Gogowitsch Nov 21 '20 at 17:52
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@Gogowitsch, good catch, very useful. key
S
adds a note andCtrl + H
highlight text. (both still require a mouse click to start writing on the annotation). – alfC Nov 22 '20 at 01:54
You could also try Okular. Now you can actually export annotations to PDFs in Okular (this was not possible until recently): http://docs.kde.org/stable/en/kdegraphics/okular/annotations.html
It seems Okular has to be built with Poppler at least version 0.20. It works with Ubuntu 13.04.
Update:
The version of Okular (0.19.3) found in at least Ubuntu 14.04 now also supports customising the review toolbar (the toolbar for adding annotations) by adding and modifying the various annotation types that can be selected.

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Xournal would be worth taking a look at. Annotations and modifications are stored in a separate file but can be easily exported to PDF.
I don't think there's any PDF editor out there that supports any kind of sophisticated math notation, but I might be mistaken.

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PDF-X-Change Viewer is fairly good. You have to run it under Wine, though.
You can read up on it here: Finally, real PDF annotating under Linux! (with help from Wine)
Or you could look at pdfedit
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There is yet another alternative. You can install Adobe Reader. The latest linux version is 9.5.5 (which is dated compared to W$ and Mac versions). It allows for editing and commenting. You do have to enable the editing and commenting toolbars (right click on the toolbar and select).
sudo apt-get install adobereader-enu
sudo apt-get -f install # needed because there is a wrong dependency
For doing proofreading when working with a publisher this is the way to go.

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I also suggest you to use adobe reader for that. Adobe reader might not be the fastest (for viewing only the default ubuntu viewer is way faster for large documents), but is available on many platforms and works very well. – ortang Jul 30 '13 at 07:31
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Our company, Qoppa Software publishes a free advanced PDF viewer for Linux. It can render many PDF features including annotations, form fields, layers. PDF Studio Viewer has advanced printing options, and other UI features such as loupe tool, pan & zoom, rulers & grid, etc. There are navigation panes such as thumbnails, comments, digital signatures, bookmarks, etc .. And the application is easy to install with no dependencies. The installer comes as a single file. https://www.qoppa.com/pdfstudioviewer/

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I'm a huge fan of Master PDF Editor, which is free for non-commercial use (home, education). Features include:
- Comment and annotate PDF documents
- Add and/or edit bookmarks in PDF files
- Edit PDF text and images
- Create and fill PDF forms
- Split and merge PDF documents
- Create new PDF document from scanner or existing file(s)

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You could give Polar Bookshelf a look.
Then note style is similar to Mendeley, where notes are shown collected in a sidebar. It also copies out highlighted text. For math, it has the very handy feature that you can drag a "highlight box" around content, with the content then shown in the list of notes.
Note that Polar stores notes etc. in a database, currently with no options to share them, and not embed option.

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For anyone who found this question, my suggestion is to use:
Foxit PDF Reader
installation link: https://www.linuxbabe.com/desktop-linux/install-foxit-pdf-reader-ubuntu
In my opinion it is a more powerful PDF reader than any mentioned in this post. Its advantages include, but are not limited to:
- user friendly interface
- easy customization
- comparable features/functions to Adobe Acrobat Reader
And the most important is that it is available cross systems: Windows, Mac and Linux.
Try it out, I believe you will find amazing!