Mosses are often treated as the poor relation in plant diversity. Popular presentations of plant evolution often tend to have even more of a Scala Natura-esque slant to them than presentations of animal evolution, and so mosses and other non-vascular plants get glossed over as mere stepping stones to their more upright "descendants", if they even warrant a mention at all. This is, of course, complete rubbish - mosses have a very respectable diversity of species (about 10,000, according to Tree of Life). I've met a few moss researchers over the years, and a more devoted following a taxon could not hope for.
Ptychomitrium muelleri is a haplolepidous moss of the family Ptychomitriaceae (I'll explain what that means in a minute). It grows to a maximum height of one and a half centimetres, and if the type specimens are any indication, prefers to grow on rocks. Ptychomitrium mosses seem to be found more or less worldwide, but Ptychomitrium muelleri itself is found in south-eastern Australia, New Caledonia, southern South America and southernmost Africa. What is interesting about this species' distriution is that it was thought to be endemic to Australia until very recently when Cao et al. (2001) established that species described from each of the other localities were conspecific with P. muelleri. As a result, P. muelleri has what might be described as a classic "Gondwanan" distribution, but I rather doubt that Gondwana had anything to do with it. After all, moss spores are very light and extremely easily dispersed, and surely it is no coincidence that all the localities where P. muelleri can be found lie roughly along the same wind belt.
The diagram of a moss life cycle above has been stole from Palaeos.com. For the nonce, the important details are these - mosses, like other plants, are multicellular at both the haploid and diploid stages of the life cycle, but unlike vascular plants, the larger, dominant stage of the life cycle is the haploid gametophyte. When a female gametophyte is fertilised, the diploid sporophyte remains attached to the gametophyte and grows a spore-filled capsule that eventually breaks open (after the loss of the protective calyptra) to release the spores. Around the mouth of the capsule is a ring of "teeth", the peristome. In basal mosses, the peristome is made up of entire cells, but in the class Bryopsida, the arthrodontous mosses (which includes the larger part of the mosses), the teeth are reduced to cell wall remnants. Most of the bryopsid lineages have two rows of teeth in the peristome, an outer and an inner, but Ptychomitrium belongs to a group called the Haplolepideae or Dicranidae which have only the inner row of teeth. The haplolepidous mosses form a monophyletic clade within the Bryopsida.
Most of the features separating moss taxa are microscopic and relate to such things as cell arrangement (which is my weaselly method of saying that I don't understand a word of them), but Ptychomitrium is distinguished by having a mitrate calyptra (and those unsure what "mitrate" means might want to look at the Taxon of the Week post of two weeks ago) with characteristic lobes around the lower edge (Hernández-Maqueda et al., 2008, compare it to a Hawaiian skirt). Ptychomitrium muelleri has (amongst other features) lingulate (tongue-shaped, I'm guessing) leaves with smooth margins, and ovoid capsules.
Cao, T., S. Guo & Y. Zhang. 2001. Distribution of Ptychomitrium muelleri (Bryopsida), with its synonyms. The Bryologist 104 (4): 522-526.
Hernández-Maqueda, R., D. Quandt, O. Werner & J. Muñoz. 2008. Phylogeny and classification of the Grimmiaceae/Ptychomitriaceae complex (Bryophyta) inferred from cpDNA. Molecular Phylogenetics and Evolution 46 (3): 863-877.