Caja

Caja is the official file manager for the MATE desktop. It allows to browse directories, preview files and launch applications associated with them. It is also responsible for handling the icons on the MATE desktop. It works on local and remote filesystems.

Pluma

Pluma is a text editor which supports most standard editor features, extending this basic functionality with other features not usually found in simple text editors. pluma is a graphical application which supports editing multiple text files in one window (known sometimes as tabs or MDI).
Pluma fully supports international text through its use of the Unicode UTF-8 encoding in edited files. Its core feature set includes syntax highlighting of source code, auto indentation and printing and print preview support.

Eye of MATE

eom or the Eye of MATE is a simple graphics viewer for the MATE desktop which uses the gdk-pixbuf library. It can deal with large images, and zoom and scroll with constant memory usage. Its goals are simplicity and standards compliance.

Atril

Atril is a simple multi-page document viewer. It can display and print PostScript (PS), Encapsulated PostScript (EPS), DJVU, DVI and Portable Document Format (PDF) files. When supported by the document, it also allows searching for text, copying text to the clipboard, hypertext navigation, and table-of-contents bookmarks.

Engrampa

Engrampa is an archive manager for the MATE environment. It allows you to: create and modify archives, view the content of an archive, view a file contained in an archive, extract files from the archive.

MATE Terminal

MATE Terminal is a terminal emulation application that you can use to perform the following actions: access a UNIX shell in the MATE environment, run any application that is designed to run on VT102, VT220, and xterm terminals.
MATE Terminal features the ability to use multiple terminals in a single window (tabs) and profiles support.