This is an excellent paper that covers the following topics:
1. What is an alga?
2. What is a species?
3. How Many Species of Organisms are There?
4. How Many Described Species of Algae are There?
5. Challenges in Counting Species.
From the abstract:
Algae have been estimated to include anything from 30,000 to more than 1 million species. An attempt is made here to arrive at a more accurate estimate using species numbers in phyla and classes included in the on-line taxonomic database AlgaeBase (<a href="http://www.algaebase.org/" title="Link to external resource: http://www.algaebase.org">http://www.algaebase.org). Despite uncertainties regarding what organisms should be included as algae and what a species is in the context of the various algal phyla and classes, a conservative approach results in an estimate of 72,500 algal species, names for 44,000 of which have probably been published, and 33,248 names have been processed by AlgaeBase to date (June 2012).