More fungi are in the Ascomycota than in the Basiomycota and they may be evolutionarily much older than the Basidiomycota. Mushroom collectors tend to ignore ascos except for edibles such as morels (Morchella species), the 'Lobster Mushroom' (Hypomyces lactifluuorum) and truffles. Many ascos are quite small and beautiful such as the ‘Eyelash Cup’ (Scutellinia scutellata), and almost all are saprotrophs: their enzymes break down organic matter and make nutrients locked within available to other living organisms. They are called ascomycetes because their mechanisms of spore formation and dispersal are unique to all the fungi in this group, whether they appear to be cup fungi or flask fungi. Ascomycetes are the dominant associate of lichens, although there are also some basidiomycete lichens. In fact lichens are fungi that have had a long term relationship with an algae, along with bacteria and in some cases, a virus.
Not all fungi have common names, and this is why we are using scientific binomials to refer to the various families and species within each family. You can simply click on a name and be brought to the photo and description of each included fungus in the Ascomycota. Remember, if a particular name is in parentheses, that is the older name which you can use to find the fungus in your favorite field guide published before 2018. To make it a bit easier to bind a particular ascomycete, I will use the color GREEN for Cup fungi and BLACK for Flask Fungi.

Scutellinia scutellata
ANNULOHYPOXYLON (See JACKROGERSELLA) multiforme
CORDYCEPS capitata (See TOLYPOCLADIUM)
DASYSCYPHUS____virgineus (See LACHNUM virgineum)
ELAPHOCORDYCEPS capitata (See TOLYPOCLADIUM)
____ophioglossoides (See TOLYPOCLADIUM)
JACKROGERSELLA (ANNULOHYPOXYLON)____cohaerens____multiforme
KRETZSCHMARIA (Ustulinia)____deusta
LACHNUM____virgineum (DASYSCYPHUS virgineus)
LEOTIA____atrovirens____lubrica____viscosa
MICROGLOSSUM____olivaceum____rufum____viride
MORCHELLA americana (esculenta)
PAECILOMYCES (ISARIA) tenuipes
PEZIZA phyllogena (badioconfusa)
_____varia
PODOSTROMA alutaceum (See TRICHODERMA aleutaceum)
PROTOCERA pallida (HYPOCREA pallida)
SPATHULARIOPSIS (SPATHULARIA) velutipes