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For diverse reasons, the taxonomy of algae is not settled yet. There is still an ongoing battle about the composition of eukaryotic supergroups and until that is resolved, it can be hard to define taxonomic levels included within supergroups.

Basis for the Classification of Algae
Algae are generally classified on the basis of the following characteristics:
Chemical and physical feature of the cell walls
Nature and properties of pigments that contribute to photosynthesis
Morphological charactersitics of cells and thalli.
Habitat
Flagella number and the location of their insertion in motile cells.
Reproductive behaviour

1. F.E. Fritsch’s Classification (1935)
2. G.M. Smith’s Classification (1950)
3. Round’s Classification (1973)
4. Bold and Wynne’s Classification (1985)
5. Robert Edward Lee’s Classification (1989)

CLASSIFICATION OF ALGAE PROPOSED BY F.E. FRITSCH (1935)

The most comprehensive and authorative classification of algae was given byF.E. Fritsch (1935) in his book ‘The Structure and Reproduction of the Algae’. His classification was based on such criteria as
pigmentation, types of flagella, assimilatory products, thallus structure and methods of reproduction.

F.E. Fritsch (1935, 1948) divided algae into 11 classes on
following basis:
Number and mode of attachment of flagella in the motile cells
Thallus structure
Chemical nature of pigments
Reserve food materials
Method of reproduction
Variation in the life cycles

11 Classes

1. Chlorophyceae
2. Xanthophyceae
3. Chrysophyceae
4. Bacillariophyceae
5. Cryptophyceae
6. Dinophyceae
7. Chloromonadineae
8. Euglenineae
9. Phaeophyceae
10. Rhodophyceae
11. Myxophyceae.

Smith’s Classification
Smith(1950)classified algae into seven divisions. These divisions
include one or more classes. He included certain algae of
uncertain position into Chloromonadales & Cryptophyceae.
1.Chlorophyta:Chlorophyceae&Charophyceae
2.Chrysophyta:Chrysophyceae,Xanthophyceae&Bacillariophyceae
3.Pyrophyta:Dinophyceae &Desmophyceae
4.Euglenophyta
5.Phaeophyta
6.Rhodophyta

7.Cyanophyta

Bold and Wynne’s Classification
Bold and Wynne(1978,1985) recognized ten divisions of algae retaining the
nomenclature given by Papenfuss(1946),exceptforblue-greenalgae. They
considered Cyanophyceae as a division and called it Cyanochloronta where as
Papenfuss had included it in phylum Schizophyta as a class

1. Cyanophyta (Blue Green Algae)
2. Prochlorophyta (Single genus: Prochloron)
3. Chlorophyta (Green algae)
4. Charophyta (Stone worts)
5. Euglenophyta
6. Phaeophyta (Brown algae)
7. Chrysophyta (Golden and yellow green algae)
8. Pyrrhophyta (Dinoflagellates)
9. Cryptophyta
10. Rhodophyta (Red algae)

Robert Edward Lee’s Classification
Lee(1989) divided the algae based on evolution and formed 4
evolutionary groups of algae which are further divided into 15
phyta(=divisions).
1.Prokaryotic algae (Cyanophyta)
2.Eukaryotic algae with chloroplast surrounded only by the two membranes of
the chloroplast envelope (Glaucophyta, Rhodophyta and Chlorophyta)
3.Eukaryotic algae with chloroplast surrounded only by one membrane of
chloroplast endoplasmic reticulum (Euglenophyta and Dinophyta)

4. Algae which have two membranes of chloroplast endoplasmic reticulum
   (Cryptophyta & Heterokontophyta)