Types of lens designs

How do you know the difference between the various types of lenses? Is it the number of elements? Is there a place that all these things are listed?

A great place to start is R. Kingslake's "History of the Photographic Lens", which makes a great read but is, unfortunately, an absurdly expensive book (~$75). View Camera had a series of articles "History of Lens Design" in four parts by Lynn Davis which was quite useful. I think these are available in PDF format (or were) on a CD which could be purchased from View Camera.

For specific lenses, the The Lens Collectors Vade Mecum provides diagram.

Bostick and Sullivan have a selective list of lenses which includes number of elements and groups.

http://www.bostick-sullivan.com/Alt_cameras/large format lenses.htm

And here is another list from Robert Monaghan's Medium Format Site:

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