DOTM is a relatively new proprietary file type that was first created for Microsoft Office 2007. This file type is used to store macro-enabled word documents, meaning that repetitive actions that the user does while editing the file can be stored and automated. Data is stored in a compressed zip format with a single xml file to keep track of all formatting, making the filesize much smaller that the preceding file formats. Data is likely to be formatted text, possibly with images and fonts stored in the file.
There are a few ways to open these files. Because the file type is proprietary, Microsoft Office 2007, 2003, and 2010 are the programs that likely have the best compatibility. However, there is a free and open source program called Open Office that has a word processor that is very compatible with dotm files. The macros that are stored in the file may not work perfectly, given that some of the functions stored in the macros may be specific to Microsoft Office, but the file and formatting will all remain identical. Open Office also has an analogue program to everything else in the Microsoft Office suite, including a presentation editor and spreadsheet editor, among others.