Two theories on the origin of the serif:
Roman letter outlines were first painted onto stone, and the stone carvers followed the brush marks, which flared at stroke ends and corners, creating serifs.
Serifs were created to neaten the ends of lines as they were chiseled into stone.
Some main classifications of type:
Old Style or Humanist serif typefaces are characterized by a low contrast in stroke weight and angled serifs (Example: Garamond)
Modern serifed typefaces broke from traditional typography of the time with a high contrast of strokes, straight serifs and a vertical axis. (example: Bodoni)
Humanist characteristics include proportions that were modeled on old style typefaces (Example: Gill Sans)
Geometric sans-serif Typfaces are based on geometric forms. For instance, the o is often a perfect circle. (Example: Futura)
These typefaces are often developed with a specific use in mind and are designed for larger point size use in headlines, posters and billboards. They are usually hard to read at small sizes. (Example: Insomnia Deco)
These are fonts whose letters and characters each occupy the same amount of horizontal space. Monospaced fonts are customary on typewriters and for typesetting computer code. (Example: Courier)
X-height: the distance between the baseline of a line of type and tops of the main body of lower case letters (i.e. excluding ascenders or descenders.