MindMup is a web-based mind mapper that you can use free, with no limit on the number of maps. It supports multi-user, simultaneous access and, if you’re using MindMup’s free storage or storing maps locally on you computer, it requires no log in.
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Roy Grubb from www.mind-mapping.org has written a detailed review of the MindMup tool which lets you create mind maps in your browser.
According to R.G., MindMup is "an attractive tool for school use", so don't miss it!