A recent multilocus phylogenetic study the has reviewed the taxonomy of the dermatophytes. 

Arthroderma now contains 21 species, Ctenomyces one species, Epidermophyton one species, Lophophyton one species, Microsporum three species, Nannizzia nine species and Trichophyton 16 species. In addition, two new genera have been introduced: Guarromyces containing one species and Paraphyton three species. Although the number of genera has increased, the species that are relevant to routine diagnostics now belong to smaller groups, which should enhance their identification. (de Hoog et al. 2017. Towards a noval multilocus phylogenetic taxonomy for dermatophytes. Mycopathologia 182: 5-31).

Identification of common dermatophytes.
Microscopic morphology of the micro and/or macroconidia is the most reliable identification character, but you need a good slide preparation and you may need to stimulate sporulation in some strains. Culture characteristics such as surface texture, topography and pigmentation are variable and are therefore the least reliable criteria for identification. Clinical information such as the site, appearance of the lesion, geographic location, travel history, animal contacts and race is also important, especially in identifying rare non-sporulation species like M. audouini, T. concentricum and T schoenleinii etc.

Species descriptions

A list of Mycology references cited for the identification of medically important fungi is available for viewing.