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The "Expert Set" is a character set invented by Adobe around 1990, which includes Latin small caps, oldstyle figure, a set of five f ligatures (fi, fl, ff, ffi, ffl), fractions and superiors. In the original meaning, an "Expert Set font" has exactly these characters, and supplements a "regular" character set font.
Expert Set fonts from other type foundries usually have the same standard character set, but some foundries have used the phrase to denote other specialized charater sets, which may or may not have some overlap with the standardized "expert set."
Expert set fonts are becoming less common with advent of OpenType which allows for these extras to be included in the same font that contains the default glyphs, accessed more easily, and inserted into a layout without damaging the underlying text.