Algae is a member of the Protista kingdom, or eukaryotes -- membrane-encased plants. Algae are generally understood as plants that lack roots, stems and leaves, which reproduce asexually. There are eight phyla of algae: diatoms, chlorophyta, euglenophyta, dinoflagellata, chrysophyta, phaeophyta, rhodophyta and cyanobacteria. There are three phyla of freshwater-only algae: diatoms, euglenophyta and chrysophyta.
Diatoms are single-celled algae, usually golden or brown in color, that form freshwater colonies that appear elaborately sculpted. Diatoms reproduce rapidly in temperate climates during spring; this is a process called an algae bloom. When the aquatic diatom algae die, the organisms drop away into the water, and leave behind these sculptures of organic material. The material can be collected as a valuable soil amendment, called diatomaceous earth. Diatoms are responsible for most of the limestone on the surface of the earth.
If you see a pond gone green adjacent to a fertilized field, chances are the dark green algae that has colonized it is eugelnophyta. Euglenophyta is a single-celled, mostly aquatic algae that reproduces by cell division. It is autotrophic, which means it makes food from light, but is also hetertrophic, which means it takes food from the environment; this is why it colonizes nitrogen-rich water. There are around 1,000 species of euglenophyta algae.
Many lakes depend on chrysophyta, because chrysophyta are the main food for zooplankton, which forms the next level of the food chain for a biodiverse lake. Chrysophyta are also called golden algae. They are primarily autotrophic, but will resort to heterotrophy in the absence of adequate light. There are around 1,000 species of chrysophyta. Some are filamentous and colonial -- they attach to things and grow colonies; and some are free-swimming algae.