A system of taxonomy of algae, the Hoek, Mann and Jahns system was published in
Hoek, C. van den, Mann, D.G. and Jahns, H.M. (1995).
Algae An Introduction to Phycology. Cambridge University Press, Cambridge. ISBN 0-521-30419-9.
Class Cyanophyceae
Order Chroococcales (e.g., Cyanothece, Aphanothece, Merismopedia, Chroococcus, Gloeocapsa, Microcystis, Chamaesiphon)
Order Pleurocapsales (e.g., Cyanocystis, Pleurocapsa)
Order Oscillatoriales (e.g., Oscillatoria, Lyngbya, Microcoleus)
Order Nostocales (e.g., Nostoc, Anabaena, Aphanizomenon, Scytonema, Rivularia)
Order Stigonematales (e.g., Stigonema)
Class Prochlorophyceae (e.g., Prochloron, Prochlorococcus, Prochlorothrix)
Class Glaucophyceae (e.g., Cyanophora, Glaucocystis)
Class Bangiophyceae
Order Porphyridiales (e.g., Porphyridium, Chroodactylon)
Order Rhodochaetales (e.g., Rhodochaete)
Order Erythropeltidales (e.g., Erythrotrichia)
Order Compsogonales
Order Bangiales (e.g., Porphyra, Bangia)
Class Florideophyceae
Order Acrochaetiales (e.g., Audouinella)
Order Palmariales (e.g., Palmaria, Rhodophysema)
Order Nemaliales (e.g., Nemalion, Galaxaura)
Order Batrachospermales (e.g., Lemanea, Batrachospermum)
Order Corallinales (e.g., Lithophyllum, Jania)
Order Hildebrandiales
Order Bonnemaisoniales
Order Gelidiales (e.g., Gelidium)
Order Gigartinales (e.g., Acrosymphyton, Dumontia, Chondrus, Mastocarpus)
Order Gracilariales
Order Ahnfeltiales
Order Rhodymeniales (e.g., Chylocladia)
Order Ceramiales (e.g., Polysiphonia, Callithamnion, Ceramium, Hypoglossum)
Class Chrysophyceae
Order Ochromonadales (e.g., Ochromonas, Pseudokephyrion, Dinobryon)
Order Mallomonadales (= Class Synurophyceae, e.g., Mallomonas, Synura)
Order Pedinellales (= Class Pedinellophyceae, e.g., Pedinella)
Order Chrysamoebidales (e.g., Rhizochrysis, Chrysarachnion)
Order Chrysocapsales (e.g., Chrysocapsa, Hydrurus)
Order Chrysosphaerales (e.g., Chrysosphaera)
Order Phaeothamniales (e.g., Phaeothamnion, Thallochrysis)
Class Parmophyceae
Order Parmales (e.g., Pentalamina)
Class Sarcinochrysidophyceae
Order Sarcinochrysidales (e.g., Ankylochrysis, Sarcinochrysis, Nematochrysis)
Genus Pelagococcus (relative of the Chrysophyceae)
Class Xanthophyceae
Order Chloramoebales (e.g., Chloromeson)
Order Rhizochloridales (e.g., Rhizochloris, Myxochloris)
Order Heterogloeales (e.g., Gloeochloris)
Order Mischococcales (e.g., Chloridella, Botrydiopsis, Characiopsis, Ophiocytium)
Order Tribonematales (e.g., Tribonema, Heterococcus, Heterodendron)
Order Botrydiales (e.g., Botrydium)
Order Vaucheriales (e.g., Vaucheria)
Class Eustigmatophyceae (e.g., Ellipsoidion, Eustigmatos [= Pleurochloris], Polyedriella, Vischeria, Chlorobotrys, Nannochloropsis)
Class Bacillariophyceae (= Diatomophyceae)
Order Pennales (e.g., Navicula, Gyrosigma, Achnanthes, Tabellaria, Nitzchia, Surirella)
Order Centrales (e.g., Coscinodiscus, Thalassiosira, Stephanodiscus, Cerataulus, Triceratium, Odontella, Rhizosolenia)
Class Raphidophyceae (e.g., Chatonella, Gonyostomum, Merotrichia, Vacuolaria, Fibrocapsa)
Class Dictyochophyceae (e.g., Dictyocha)
Class Phaeophyceae
Order Ectocarpales (e.g., Phaeostroma, Spongonema, Ectocarpus)
Order Sphacelariales (e.g., Sphacelaria)
Order Syringodermatales
Order Dictyotales (e.g., Dictyota)
Order Scytosiphonales (e.g., Scytosiphon)
Order Cutleriales (e.g., Cutleria)
Order Dictyosiphonales (e.g., Dictyosiphon)
Order Chordariales (e.g., Sphaerotrichia, Liebmania, Elachista)
Order Sporochnales
Order Desmarestiales (e.g., Desmarestia)
Order Laminariales (e.g., Laminaria, Chorda)
Order Fucales (e.g., Fucus, Hormosira)
Order Durvillaeales (e.g., Durvillaea)
Order Ascoseirales
Class Bicocoecida (e.g., Pseudobodo, Cafeteria)
Class Oomycetes (e.g., Phytophthora)
Class Hyphochytridiomycetes
Class Labyrinthulomycetes
Class Haptophyceae
Order Prymnesiales (e.g., Chrysochromulina, Prymnesium, Corymbellus, Phaeocystis)
Order Isochrysidales (e.g., Chrysotila, Pleurochrysis [= Hymenomonas])
Order Coccolithophorales (e.g., Emiliania, Syracosphaera, Discosphaera)
Order Pavlovales (e.g., Pavlova)
Class Cryptophyceae (e.g., Cryptomonas, Chilomonas, Bjornbergiella)
Class Dinophyceae
Order Gymnodiniales (e.g., Gymnodinium, Symbiodinium, Polykrikos)
Order Gloeodiniales (e.g., Gloeodinium)
Order Thoracosphaerales (e.g., Thoracosphaera)
Order Phytodiniales (= Dinococcales, e.g., Phytodinium)
Order Dinotrichales (e.g., Dinoclonium)
Order Dinamoebidales (e.g., Stylodinium, Dinamoebidium)
Order Noctilucales (e.g., Noctiluca)
Order Blastodiniales (e.g., Blastodinium)
Order Syndiniales
Order Peridiniales (e.g., Peridinium, Protoperidinium, Ceratium, Gonyaulax)
Order Dynophysiales (e.g., Dinophysis, Triposolenia, Amphisolenia, Ornithocercus, Histioneis)
Order Prorocentrales (e.g., Prorocentrum)
Class Euglenophyceae
Order Euglenales (e.g., Euglena, Astasia)
Order Eutreptiales
Order Euglenamorphales
Order Rhabdomonadales
Order Sphenomonadales
Order Heteronematales
Class Chlorarachniophyceae (e.g., Chlorarachnion)
Class Prasinophyceae
Order Mamiellales (e.g., Mamiella, Bathycoccus)
Order Pseudoscourfieldiales (e.g., Nephroselmis)
Order Pyramimonadales (e.g., Pyramimonas, Halosphaera, Pachysphaera [?], Pterosperma [?], Mesostigma [?])
Genus Pedinomonas (sometimes classified in the class Pedinophyceae, or Loxophyceae)
Order Chlorodendrales (e.g., Tetraselmis)
Class Chlorophyceae
Order Volvocales [including the Tetrasporales] (e.g., Chlamydomonas, Chlorogonium, Hyalogonium, Gloeomonas, Diplostauron, Polytoma, Carteria, Brachiomonas, Lobomonas, Sphaerellopsis, Haematococcus, Phacotus, Pteromonas, Stephanosphaera, Gonium, Pandorina, Eudorina, Volvox, Pseudosphaerocystis)
Order Chlorococcales (e.g., Chlorococcum, Golenkinia, Chlorella, Chodatella, Oocystis, Kirchneriella, Nephrocytium, Actinastrum, Crucigenia, Sphaerocystis, Coccomyxa, Scenedesmus, Hydrodictyon, Pediastrum, Chlorosarcinopsis, Cylindrocapsa, Geminella, Binuclearia, Radiofilum, Sphaeroplea, Characiosiphon, Atractomorpha)
Order Chaetophorales (e.g., Uronema, Stigeoclonium, Draparnaldia, Schizomeris)
Order Oedogoniales (e.g., Oedogonium)
Class Ulvophyceae
Order Codiolales (e.g., Chlorocystis, Ulothrix, Spongomorpha, Urospora, Acrosiphonia, Monostroma)
Order Ulvales (e.g., Ulva, Enteromorpha, Ulvaria, Acrochaete)
Class Cladophorophyceae
Order Cladophorales (e.g., Cladophora, Chaetomorpha, Rhizoclonium, Struvea, Valonia, Siphonocladus, Dictyosphaeria)
Class Bryopsidophyceae
Order Bryopsidales (e.g., Bryopsis, Pseudobryopsis, Derbesia, Codium)
Order Halimedales (e.g., Udotea, Penicillus, Halimeda, Caulerpa)
Class Dasycladophyceae
Order Dasycladales (e.g., Acetabularia, Batophora, Dasycladus, Neomeris, Cymopolia)
Class Trentepohliophyceae
Order Trentepohliales (e.g., Trentepohlia, Cephaleuros)
Class Pleurastrophyceae
Order Pleurastrales (e.g., Trebouxia, Myrmecia, Friedmannia, Pleurastrosarcina, Pleurastrum, Microthamnion)
Position uncertain:
Order Prasiolales (e.g., Prasiola)
Class Klebsormidiophyceae
Order Klebsormidiales (e.g., Chlorokybus, Raphidonema, Klebsormidium)
Order Coleochaetales (e.g., Chaetosphaeridium, Coleochaete)
Class Zygnematophyceae
Order Zygnematales (e.g., Spirogyra, Mougeotia, Zygnema, Spirotaenia, Cylindrocystis, Netrium)
Order Desmidiales (e.g., Cosmarium, Gonatozygon, Closterium, Pleurotaenium, Tetmemorus, Euastrum, Micrasterias, Cosmocladium, Xanthidium, Staurastrum, Desmidium, Hyalotheca, Spondylosium, Sphaerozosma, Onychonema)
Class Charophyceae
Order Charales (e.g., Chara, Lamprothamnium, Nitellopsis, Nitella, Tolypella)
In a note added in proof, an alternative classification is presented for the class Chlorophyceae:
Class Chlamydophyceae
Order Volvocales
Order Chaetophorales
Order Chlorococcales (e.g., Chlorococcum, Chlorosarcinopsis, Cylindrocapsa [?])
Class Chlorophyceae
Order Chlorellales (e.g., Chlorella, Kirchneriella, Scenedesmus, Hydrodictyon, Pediastrum, Sphaeroplea, Atractomorpha)
Class Oedogoniophyceae
Order Oedogoniales (e.g., Oedogonium)
Many examples of genus given in the book could not be assigned to one of these classes, because the ultrastructural characteristics needed for their classification have not yet been studied.
