The Hoek, Mann and Jahns system is a system of taxonomy of algae. It was first published in Algae: An Introduction to Phycology by Cambridge University Press in 1995.

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• 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)