You can make a map with pen and paper, or by moving around post-it notes with concepts written on them. If you prefer a computer screen there are a number of software options that allow you to draw or connect shapes together, like Microsoft PowerPoint or Google diagrams. The first software designed specifically for making and sharing concept maps, and the one that I always recommend, is called CmapTools.
CmapTools is freely available for download from IHMC, the Institute for Human and Machine Cognition. The software is supported with extensive help files that offer step-by-step instructions with screenshots from the program, as well as videos. Get tips on CmapTools functionalities from our Cmap.
CmapTools is designed without a lot of the bells and whistles that can get in the way of the task at hand: making maps. It is easy to create concepts but it takes some time to get used to connecting boxes and moving them around. The style options allow you to change things like the size and colour of words and objects, as you can see on the examples page.
The wonderful thing that IHMC offers is free server space. This means that you can create a folder on one of their public servers and save your maps there. You will then have links that you can share with others. It takes some time to load information from a public server so the best thing to do is to set the folder as one of your favourites to make it easily accessible. We created a McGill Library folder on IHMC Public Cmaps that you are welcome to use.
The other great thing about this software, is that it allows you to add resources and web addresses to individual concepts. This helps with organizing documentation and important sources, but also turns concept maps into great presentation tools that can shared.
You may also be interested in learning about IHMC's other products: CmapTools for iPad, Cmap Cloud, and CmapTools in the Cloud.
These options are not specifically designed for concept mapping but they can be used to create maps with connected concepts.