There is a very limited choice when it comes to vector based image editors. In fact Inkscape is now probably the only viable free one around now (please do let us know if you know of any others).On top of that I am probably not a good choice to do a review of a vector based program as I have very limited experience with them. This is something I intend to correct over the coming months.
The majority of images we come across are bitmap ones, this means they are made up of tiny pixels/dots and all the information on the colour/ transparency etc of each pixel is saved in the image format. There are however a sizeable number of images around of a different type, these are “Vector Images” which are made up of objects. In a vector based editing program each object can be edited separately.
Now the benefit of a vector images is that it can be resized indefinitely without the loss of any image quality. Also the files tend to be a lot smaller as there is a lot less information to be held. (If you are an inquisitive person like me try opening a vector graphic in a text editor, you will find the code is actually readable although you’d have to be a much better mathematician than me for it to make sense to you). For these reason they are often for items such as logos. Whilst being able to use the logo on a letterhead without a problem it could still be blown up to the size of a advertising hoarding without loosing any quality. Inkscape if fully compatible with common vector image formats such as SVG.
If you want to learn vector imaging the the Inkscape vector image program is a great for you. There website has a full set of tutorials (written and videos) so there is no shortage of material to get you started. If you have already learnt vector imaging at school, college or work and want to carry on without the expense of proprietary software, again, this should come in very handy.
You can get Inkscape here: http://www.inkscape.org/en/download/
Available for Windows, OSX and Linux.
As with any software, when at all possible you should download direct from the official website.