An area cartogram is a thematic map that uses area as a symbol to present certain attribute values. There are many different methods and algorithms to create area cartograms. We identify more than 30 algorithms that have been proposed by researchers since 1973. These algorithms can be categorized into four main types: non-contiguous, contiguous, Dorling and pseudo-cartogram. Within these four types, contiguous cartogram is the most common one, which aims to keep balance between preserving relative location and minimizing shape distortion. Given the variety of algorithms, not many have been included in GIS software packages or public domain software. This research collects several different algorithms and uses them to create a series of maps. We investigate the difference of these maps by comparing their geometric properties and topology. We also investigate the cognition aspect of this issue by testing the reactions of map readers. It is anticipated that such research can enhance the development of area cartogram and help promote its application.