Corydalis is a genus of about 300 species some people consider to belong to Fumariaceae family. Others chose to include this family as a subfamily, Fumarioideae, in the Papaveraceae family. This genus is widely distributed in the Northern Hemisphere, including Europe, Asia, North America, and the mountains of Africa. Some have tubers or enlarged rhizomes, and others are strictly fibrous-rooted. The former are handily divided into woodland and scree species, for purposes of cultivation. The genus name comes from the Greek korydalís "crested lark" which roughly represents the characteristic flower shape. An excellent reference book on the geophytic species of this genus was written by Magnus Lidén and Henrik Zetterlund in 1997. A more recent (2008) guide for the genus and related genera was written by Mark Tebbitt, Lidén, and Zetterlund.
The tuberous species in particular are often grown in bulb collections and are propagated by increase of the tubers (typically slow) or by seed (which germinates best if sown fresh). Seeds collected and sown within the year at the beginning of fall (September-October) usually yields good germination. Seeds should be stored in moist sand, which seems to help with viability. Many beautiful images of the geophytic forms can be seen on John Lonsdale's website.
The table below contains links to pages describing each species separately. To see all the species together visit Corydalis Species.