Notes on the Classification of Organisms
Organismal diversity is the product of evolution.
Evolutionary paths are branched and numerous, though most arrive at dead ends with organisms which do not survive environmental change. We will consider these evolutionary paths (called lineages), and  the processes that carry organisms along them.
While the lineage of any given organism may have twisted repeatedly according to the whims of chance and change, key nodes may nevertheless be tracked retrospectively. These nodes consist of times of identifiable change, particularly points of divergence between two lineages (speciation events). The delineation of these nodes in organismal lineages is accomplished through fossil reconstruction of the past as well as by comparing extant organisms, looking for similarities and differences in anatomies, physiologies, genes, behaviors, etc. From this information classification and phylogenetic reconstruction is accomplished.
In this lecture we will review the general way on how organisms are systematically classified, in addition we will attempt to compare how the classification of living organisms compares with that of fossils forms.

Some basic rules for the classification of organisms:
In order to make sense of the diversity of organisms, it is necessary to group similar organisms together and organize these groups in a non-overlapping hierarchical arrangement.

Taxonomy is the science of biological classification.
The basic taxonomic group is the species, which is defined in terms of either sexual reproduction or general similarity.
Morphological, physiological, metabolic, ecological, genetic, and molecular characteristics are all useful in taxonomy because they reflect the organization and activity of the genome. Nucleic acid structure is probably the best indicator of relatedness because nucleic acids are either the genetic material itself or the products of gene transcription.

Classifications are based on any analysis of possible evolutionary relationships (phylogenetic or phyletic classification) or on overall similarity (phenetic classification).

Linnaeus, Carolus (late 1700s) system of classification according to similarity: Carolus Linnaeus developed a system of classification of every known organism up to that time. This system is based on creating and differentiating groups in terms of structural (and other) similarities and differences. Linnaeus also invented binomial nomenclature to keep track of group members. That is the use of Genus and species names for all the organisms, e.g. Home sapiens for humans.

Systematics is the study of the diversity of organisms and their evolutionary relationships.
Science of classification: Systematics is the science of the classification of organisms. The main goal of systematics is the discovery and codification of phylogenetic relationships between organisms.

The term systematics often is used for taxonomy. However, many taxonomists define it in more general terms as 'the scientific study of organisms with the ultimate object of characterizing and arranging them in an orderly manner.' Any study of the nature of organisms, when the knowledge gained is used in taxonomy, is a part of systematics. Thus systematics encompasses disciplines such as morphology, ecology, epidemiology, biochemistry, molecular biology, and physiology.

Taxon (pl. taxa), A taxon is a phylogenetic grouping of organisms. There are two related processes in taxonomy. Taxonomy is the science concerned with the identification, classification, nomenclature of organisms.

Taxonomy [Greek taxis, arrangement or order, and nomos, law, or nemein, to distribute or govern] is defined as the science of biological classification. In a broader sense it consists of three separate but interrelated parts: classification, nomenclature, and identification.
Note that the terms systematics and taxonomy can often be used semantically in a nearly indistinguishable manner.

Identification is the practical side of taxonomy, the process of determining that a particular (organism) belongs to a recognized taxon.

Classification is the arrangement of organisms into groups or taxa.

Nomenclature is the branch of taxonomy concerned with the assignment of names to taxonomic groups in agreement with published rules.
Note that ideally names have taxonimic meaning, i.e., they give clues to phylogenetic relationships.

Hierarchical classification The full description of a given organism's place among all the world's organisms does not end with its binomial designation. There exists a hierarchy of designations only the last of which describe genera and species denomination. A category in any rank unites groups in the level below it based on shared properties. The major designations, listed in terms of increasing specificity, include:

domain (empire/super-kingdom)

Phylogeny [phylogenetic group]
A phylogeny is a representation of organisms based on and describing evolutionary relationships.

A phylogenitic group (i.e., taxon) all of whose members are descended from a common ancestor which is a member of the same phylogenitic group, and which consists of all of the (known or considered) descendants of that common ancestor.
A monophyletic taxon is a good taxon in an evolutionary sense, meaning that no members which ought to be a part of the taxon, in terms of ancestor-descendant relationships, are excluded.

Symbolic examples:
For example, if both B and C are descendants of A, then a monophyletic taxon would consist of all three species.
For example, if both C and D are descendants of B, and B is a direct descendant of A, then a monophyletic taxon of these species could consist either of all four species, or of just species B, C, and D.

A phylogenitic group (i.e., taxon) all of whose members are descended from a common ancestor, but in which one or more common ancestor is not a member of the same phylogenitic group, and that missing common ancestor is the most recent common ancestor.

Paraphyletic (Missing member)
A phylogenitic group (i.e., taxon) all of whose members are descended from a common ancestor, but which does not include all of the known or considered descendants of that common ancestor. In the usage of cladists, a paraphyletic taxon is a monophyletic taxon in which a member, other than the most recent common ancestor, is excluded. Typically paraphyletic taxa represent the improper exclusion of members on the basis of phenotypic differences rather than on the basis of ancestor-descendant relationships.

The purpose of phylogenetic studies is to establish the evolutionary relationships among different species. In particular, we are interested in the identification of natural clades. A clade is defined as a group of species that share a common ancestor, which is not shared by another species outside of the clade.
Monophylectic taxon:
In other words, a clade is a monophyletic taxon.
Clades are the only phylogenetically/evolutionarily real taxons.
Other, non-monophyletic (e.g., paraphyletic) taxons are based on, for example, just morphological similarities rather than evolutionary relationships.

Example: reptiles do not form a natural clade:
The reptiles do not represent a true clade because, while there may be strong evolutionary relationships within this group, there are also a number of taxa which evolved from within this taxa but which are not included in the taxa reptiles
Examples of these latter taxa include the birds, the mammals, and the dinosaurs as well as a number of extinct lineages.

Example: apes + humans form a clade:
The designation apes, like reptiles, does not form a true clade, though here this problem is easily corrected simply by accepting that humans are modified apes (just as apes are modified mammals and mammals are modified reptiles and reptiles are modified amphibians and amphibians are modified fish, etc.). That is, humans plus those animals typically classified as apes together form a monophyletic taxon, i.e., a clade.

3. Classification of Organisms: Typological (base on the type specimen)
    a. The Species Concept
        i. Biological
        ii. Paleontological
    b. Basis for classification = Evolution
        i. Hierarchy of classification
            1. Domain> Kingdom> Phylum (or Division)> Class> Order> Family> Genus (pl. Genera)> Species
        ii. Classification of humans
            1. Domain: Eucarya
            2. Kingdom: Animalia
            3. Phylum: Chordata(Plants use Division instead of Phylum)
            4. Class: Mammalia
            5. Order: Primates
            6. Family: Hominidae
            7. Genus: Homo
            8. Species: Homo sapiens
        iii. Domains:
            1. Bacteria: heterotrophic, cyanobacteria (stromatolites)
            2. Archaea: halophiles, thermophiles
            3. Eucarya
                a. Kingdom Protista
                b. Kingdom Fungi
                c. Kingdom Animalia
                d. Kingdom Plantae
        iv. Taxonomy: the study of the composition and relationships of those groups. Taxon individual group (pl. taxa)
        v. Species: group of individuals that can interbreed.