Topographic Map

http://en.wikipedia.org/wiki/File:Hawaii_Island_topographic_map-fr.svg

Above is an example of a topographic map which simply is used to depict different levels of elevation.  Topographic maps may come in color or in black and white and the lines around it signify different elevations and as you can see depicted above the elevation increases as you move inward as indicated by the darker coloration.  It focuses on large scale detail and is not only used to show natural features, but even man made ones. (5/22)

Planimetric Map

 http://blog.justroughinit.com/avoid-getting-lost-carry-a-map/?nomo=true

This is a perfect example of a planimetric map which shows geographic entities and features of the Earth's surface in this region minus the roads, buildings as well as bodies of water which may be visible from above.   It focuses more on features such as sidewalks, streets, highways, reservoirs, tanks, airports and bridges for instance.  Illustrated above is a map that leads to Mount Washington and the planimetric map is typically used as a base map and is used interchangeably with another term known as a line map.

Mental Map

http://www.google.com/imgres?imgurl=http://2.bp.blogspot.com/-Y6kIX9erPvg/Ta8FF1u2KWI/AAAAAAAAABI/w_UqJsKvIL0/s1600/mental%2Bmap%2B1.jpg&imgrefurl=http://elliottvolin.blogspot.com/2011/04/mental-map.html&usg=__DxZiF5Gm_og0fNvwbPAceBmZvP0=&h=270&w=432&sz=32&hl=en&start=0&zoom=1&tbnid=Ecc_GQrlee5c1M:&tbnh=135&tbnw=216&ei=01zZTZzCPKHV0QHEr938Aw&prev=/search%3Fq%3Dmental%2Bmap%26um%3D1%26hl%3Den%26sa%3DN%26biw%3D1280%26bih%3D834%26tbm%3Disch&um=1&itbs=1&iact=rc&dur=527&sqi=2&page=1&ndsp=23&ved=1t:429,r:10,s:0&tx=31&ty=37
This is an example of a mental map which illustrates someone's perspective of the world.  Mental maps are used based off experiences and memory and may not be accurate to the tee, but does accurately represent a broad perspective about what the world looks like when it comes to the shape of each of the continents as well as the locations.  This is a flat map projection that of course in one way distorts the world whether it is through direction, shape, area or distance. (05/22)