A system of taxonomy of the cryptogams, the Smith system was published in:

Smith, G.M. (1938). Cryptogamic Botany, vol. 1. Algae and fungi. McGraw-Hill, New York.

Smith, G.M. (1955). Cryptogamic Botany, vol. 2. Bryophytes and pteridophytes. 2nd ed. McGraw-Hill, New York.

Division Chlorophyta

• Class 1. Chlorophyceae

• Order 1. Volvocales

• Family 1. Chlamydomonadaceae
• Family 2. Volvocaceae

• Order 2. Tetrasporales
• Order 3. Ulotrichales

• Family 1. Ulotrichaceae
• Family 2. Microsporaceae
• Family 3. Cylindrocapsaceae
• Family 4. Chaetophoraceae
• Family 5. Protococcaceae
• Family 6. Coleochaetaceae
• Family 7. Trentepohliaceae

• Order 4. Ulvales

• Family 1. Ulvaceae
• Family 2 Schizomeridaceae

• Order 5. Schizogoniales

• Family Schizogoniaceae

• Order 6. Cladophorales

• Family 1. Cladophoraceae
• Family 2. Sphaeropleaceae

• Order 7. Oedogoniales

• Family Oedogoniaceae

• Order 8. Zygnematales

• Family 1. Zygnemataceae
• Family 2. Mesotaeniaceae
• Family 3. Desmidiaceae

• Order 9. Chlorococcales

• Family 1. Chlorococcaceae
• Family 2. Endosphaeraceae
• Family 3. Characiaceae
• Family 4. Protosiphonaceae
• Family 5. Hydrodictyaceae
• Family 6. Oöcystaceae
• Family 7. Scenedesmaceae

• Order 10. Siphonales

• Family 1. Bryopsidaceae
• Family 2. Caulerpaceae
• Family 3. Halicystaceae
• Family 4. Codiaceae
• Family 5. Derbesiaceae
• Family 6. Vaucheriaceae
• Family 7. Phyllosiphonaceae

• Order 11. Siphonocladiales

• Family 1. Valoniaceae
• Family 2. Dasycladaceae

• Class 2. Charophyceae

• Order Charales

• Family Characeae

Division Euglenophyta

• Order 1. Euglenales
• Order 2. Colaciales ( Euglenocapsales)

Division Pyrrophyta

• Class 1. Cryptophyceae
• Class 2. Desmokontae
• Class 3. Dinophyceae

• Order 1. Gymnodiniales
• Order 2. Peridiniales
• Order 3. Dinophysidales
• Order 4. Rhyzodiniales
• Order 5. Dinocapsales
• Order 6. Dinotrichales
• Order 7. Dinococcales

Division Chrysophyta

• Class 1. Xanthophyceae ( Heterokontae)

• Order 1. Heterochloridales
• Order 2. Rhizochloridales
• Order 3. Heterocapsales
• Order 4. Heterotrichales
• Order 5. Heterococcales
• Order 6. Heterosiphonales

• Class 2. Chrysophyceae

• Order 1. Chrysomonadales

• Suborder 1. Cromulinae
• Suborder 2. Isochrysidineae
• Suborder 3. Ochromonadineae

• Order 2. Rhizochrysidales
• Order 3. Chrysocapsales
• Order 4. Chrysotrichales
• Order 5. Chrysosphaerales

• Class 3. Bacillariophyceae

• Order 1. Centrales
• Order 2. Pennales

Division Phaeophyta

• Class 1. Isogeneratae

• Order 1. Ectocarpales
• Order 2. Sphacelariales
• Order 3. Tilopteridales
• Order 4. Cutleriales
• Order 5. Dictyotales

• Class 2. Heterogeneratae

• Subclass 1. Haplostichineae

• Order 1. Chordariales
• Order 2. Sporochnales
• Order 3. Desmarestiales

• Subclass 2. Polystichineae

• Order 1. Punctariales
• Order 2. Dictyosiphonales
• Order 3. Laminariales

• Class 3. Cyclosporeae

• Order Fucales

Division Cyanophyta

• Class Myxophyceae ( Cyanophyceae)

• Order 1. Chroococcales
• Order 2. Chamaesiphonales
• Order 3. Hormogonales

Division Rhodophyta

• Class Rhodophyceae

• Subclass 1. Bangioideae

• Order Bangiales

• Subclass 2. Florideae

• Order 1. Nemalionales
• Order 2. Gelidiales
• Order 3. Cryptonemiales
• Order 4. Gigartinales
• Order 5. Rhodymeniales
• Order 6. Ceramiales

Division Myxothallophyta

• Class 1. Myxomycetae

• Subclass 1. Endosporeae
• Subclass 2. Exosporeae

• Class 2. Phytomyxinae
• Class 3. Acrasieae

Division Eumycetae

• Class 1. Phycomycetae

• Order 1. Chytridiales

• Family 1. Rhizidiaceae
• Family 2. Olpidiaceae
• Family 3. Synchytriaceae
• Family 4. Cladochytriaceae
• Family 5. Woroninaceae

• Order 2. Blastocladiales
• Order 3. Monoblepharidales
• Order 4. Ancylistales
• Order 5. Saprolegniales

• Family 1. Saprolegniaceae
• Family 2. Leptomitaceae
• Family 3. Pythiaceae

• Order 6. Peronosporales
• Order 7. Mucorales
• Order 8. Entomophthorales

• Class 2. Ascomycetae

• Subclass 1. Protoascomycetae
• Subclass 2. Euascomycetae

• Order 1. Aspergillales
• Order 2. Erysiphales
• Order 3. Hysteriales
• Order 4. Phacidiales
• Order 5. Pezizales
• Order 6. Tuberales
• Order 7. Helvellales
• Order 8. Exoascales
• Order 9. Hypocreales
• Order 10. Sphaeriales
• Order 11. Dothidiales
• Order 12. Laboulbeniales

• Class 3. Basidiomycetae

• Subclass 1. Eubasidii

• Order 1. Agaricales ( Hymenomyceatae)
• Order 2. Lycoperdales ( Gasteromycetae)
• Order 3. Dacryomycetales
• Order 4. Tremellales
• Order 5. Auriculariales

• Subclass 2. Hemibasidii

• Order 1. Urediniales
• Order 2. Ustilaginales

• Family 1. Ustilaginaceae
• Family 2. Tilletiaceae

• Class 4. Fungi imperfecti
• Lichens

• Subclass 1. Ascholichenes
• Subclass 2. Basidiolichenes

Division Bryophyta

• Class 1. Hepaticae (liverworts)

• Order 1. Sphaerocarpales

• Family 1. Sphaerocarpaceae
• Family 2. Riellaceae

• Order 2. Marchantiales

• Family 1. Ricciaceae
• Family 2. Corsiniaceae
• Family 3. Targioniaceae
• Family 4. Monocleaceae
• Family 5. Marchantiaceae

• Order 3. Jungermanniales

• Suborder 1. Metzgerineae
• Suborder 2. Jungermannineae

• Order 4. Calobryales

• Class 2. Anthocerotae (hornworts)

• Order 1. Anthocerotales

• Class 3. Musci (mosses)

• Subclass 1. Sphagnobrya
• Subclass 2. Andreaeobrya
• Subclass 3. Eubrya

Division Psilophyta

• Class 1. Psilophytinae (psilophytes)

• Order 1. Psilophytales

• Family 1. Rhyniaceae
• Family 2. Psilophytaceae
• Family 3. Pseudosporochnaceae
• Family 4. Zosterophyllaceae
• Family 5. Asteroxylaceae

• Order 2. Psilotales

Division Lepidophyta

• Class 1. Lycopodinae (lycopods)

• Order 1. Lycopodiales

• Family 1. Protolepidodendraceae
• Family 2. Lycopodiaceae

• Order 2. Selaginellales

• Family 1. Selaginellaceae
• Family 2. Miadesmiaceae

• Order 3. Lepidodendrales

• Family 1. Lepidodendraceae
• Family 2. Lepidocarpaceae
• Family 3. Bothrodendraceae
• Family 4. Sigillariaceae

• Order 4. Isoetales

• Family 1. Pleuromeiaceae
• Family 2. Isoetaceae

Division Calamophyta

• Class 1. Equisetinae (horsetails)

• Order 1. Hyeniales
• Order 2. Sphenophyllales
• Order 3. Equisetales

• Family 1. Calamitaceae
• Family 2. Equisetaceae

Division Pterophyta

• Class 1. Filicinae (ferns)

• Subclass 1. Primofilices (or Inversicatenales, Coenopterideae, Palaeopteridales)

• Order 1. Protopteridales

• Family 1. Protopteridaceae
• Family 2. Cladoxylaceae

• Order 2. Coenopteridales

• Family 1. Zygopteridaceae
• Family 2. Botryopteridaceae
• Family 3. Anachoropteridaceae

• Order 3. Archaeopteridales

• Subclass 2. Eusporangitae

• Order 1. Ophioglossales
• Order 2. Marattiales

• Subclass 3. Leptosporangiatae

• Order 1. Filicales

• Family 1. Osmundaceae
• Family 2. Schizaeaceae
• Family 3. Gleicheniaceae
• Family 4. Matoniaceae
• Family 5. Dipteridaceae
• Family 6. Hymenophyllaceae
• Family 7. Cyatheaceae
• Family 8. Dicksoniaceae
• Family 9. Polypodiaceae
• Family 10. Parkeriaceae

• Order 2. Marsileales
• Order 3. Salviniales