Green algae along with brown (Division Phaeophycophyta) and red algae (Division Rhodophycophyta) are ancient groups that date back to Archean time (over 3 billion yrs. ago). Masses of algal mats trap sediments and have collectively been known as stromatolites.

Division BRYOPHYTA (the mosses, hornworts, and liverworts) 

They are the most primitive of green plants and are not important in the geological record.

These are the vascular plants with well developed conductive tissues which carry water and organic materials.

Subdivision PSYLOPHYTA (the psylophytes) 
These are the earliest and most primitive plants.  They were small, one foot or less, branched, seedless, and were not differentiated into roots, stems and leaves.  Some botanists separate the early fossil plants from the Psylophytes and give them a separate subdivision, although this arrangement is not followed here.

Subdivision LYCOPODOPHYTA (the lycophytes) 
This group separated early into two major evolutionary lines.  One line, the club mosses remained grasslike.  The other line, the Lepidodendrales became one of the dominant forms in the coal forest of the Carboniferous and became extinct at the end of the Permian.  Fossil trunks and roots show characteristic leaf and rootlet scars. More Lycophytes

Subdivision SPHENOPHYTA (the sphenophytes) 
Their record extends back to the Permian.  This group also was an important component of the Carboniferous coal forests, with some members reaching over 50' in height.  In general appearance they resembled (except for size) the modern horsetail Equisetum.  The jointed trunk pattern seen in Calamites is characteristic of the group. 

Subdivision FILICOPHYTA (the true ferns) 
Although they are common members of many floras they do not have great geological     importance. 

Subdivision SPERMATOPHYTA (the spermatophytes or seed plants) 
The first four classes which follow are often called the gymnosperms or plants with naked seeds.

Class PTERIDOSPERMOPHYTA (the pteridosperms)
The pteridosperms are often referred to as seed ferns.  These plants have a fern-like foliage, but, in contrast to true ferns, they bear seeds.  They were the most common components of the great coal forests of the Carboniferous.

More pteridosperms

Class CONIFEROPHYTA (conifers, pines, junipers, spruces, larches, cypresses, and redwoods) 
Most people are familiar with this class.  Then, as now, they were the largest and often the most common components of forests.  They were most common in the Mesozoic. 

More conifers

Class CYCADOPHYTA (the cycads) 
The cycads bear a superficial resemblance to palms. A common ornamental cycad in the South (Cycas revolutus) is called a Sago Palm.  They were so common in the Mesozoic that this period of time is often called the Age of Cycads.  They were one of the foods for herbivorous dinosaurs. They are much less common now.

 
Class GINKGOPHYTA (the ginkgoes or maidenhair trees) 
Maidenhair trees were common in the Mesozoic as a class, but are represented by only a single species now.  The leaf shape of this class is quite distinctive. 

Class ANGIOSPERMOPHYTA (the flowering plants)
As the name indicates, they bear flowers.  They appear in Cretaceous time and their rapid evolutionary rise has made them the dominant component of modern floras.  Their association with insects is essential. Some 65% of flowering plants depend on insects for pollination and hence reproduction.  There are two subclasses of flowering plants: 

Subclass MONOCOTYLEDONAE, the monocots: palms, orchids, grasses and cereals

Subclass DICOTYLEDONAE, the dicots: which includes most broad leaf trees.
More dicots