Francis Thibaudeau's system for the classification of type faces published in the early 1920's in Paris was based on the varying shapes of the serifs, and any complete description of a type face will, of course, include notes on the serifs, unless the face happens to be one of the large category of sans serifs!
The term serifs is used to describe the cross-strokes which finish the stems or arms of letters. They are usually drawn at right angles or obliquely to these stems or arms and may extend on both sides or only on one side. The stem of a letter may be the straight or oblique stroke of a capital or lower-case letter and the arms may belong, for example to a capital E or a lower-case k.
These finishing strokes will vary very considerably in shape and size. Some may be bracketed--our first diagram on the opposite page shows exactly what is meant by this term--or unbracketed, wedge-shaped or triangular (forms met respectively in types like Wide Latin and as terminals of the thin strokes in the fat faces). They may be cupped, hairline, fine slab, or heavy slab with or without bracketing.
All serifs are not flat on their undersides. Some are cupped or curved as in the AmericanType Founders Cloister, Monotype 'Garamond' Series 156, and Monotype Poliphilus. The diagrams on the opposite page will help to make these brief notes clear. Students who wish to delve deeply into the subjects of stress, of serifs, and of the nomenclature of letter forms should read Mr Joseph Thorp's TOWARDS A NOMENCLATURE OF LETTER FORMS which appeared in The Monotype Recorder. Volume 30. April/ May 1931, & the other excellent articles by the same author which appeared in subsequent issues of the same publication.