APG III system

The APG III system of flowering plant classification is the third version of a modern, mostly molecular-based, system of plant taxonomy being developed by the Angiosperm Phylogeny Group (APG). Published in 2009, it was superseded in 2016 by a further revision, the APG IV system. 
Along with the publication outlining the new system, there were two accompanying publications in the same issue of the Botanical Journal of the Linnean Society. The first, by Chase & Reveal, was a formal phylogenetic classification of all land plants (embryophytes), compatible with the APG III classification. As the APG have chosen to eschew ranks above order, this paper was meant to fit the system into the existing Linnaean hierarchy for those that prefer such a classification. The result was that all land plants were placed in the class Equisetopsida, which was then divided into 16 subclasses and a multitude of superorders. The second, by Haston "et al.", was a linear sequence of families following the APG III system (LAPG III). 
This provided a numbered list to the 413 families of APG III. A linear sequence is of particular use to herbarium curators and those working on floristic works wishing to arrange their taxa according to APG III.
Organization.
The APG III system recognized all of the 45 orders of the previous system, as well as 14 new ones. The order Ceratophyllales was erroneously marked as a new order, as it had been recognized in both of the previous APG systems. The newly recognized orders were:
The designation of alternative "bracketed families" was abandoned in APG III, because its inclusion in the previous system had been unpopular. APG III recognized 413 families, 43 fewer than in the previous system. Forty-four of the 55 "bracketed families" were discontinued, and 20 other families were discontinued as well.
The discontinued bracketed families were: 
The other discontinued families were: 
21 families were accepted in the APG III system which had not been in the previous system, and a few families were moved to a different position. The newly recognized families are:
The number of families not placed in any order was reduced from 39 to 10. Apodanthaceae and Cynomoriaceae were placed among the angiosperms, incertae sedis, that is, not in any group within the angiosperms. Eight other families were placed incertae sedis in various supra-ordinal groups within the angiosperms. The families not placed in any order were: 
The paragraph below shows the number of families in each order and the placement of those families that were not included in any order. These figures were produced by simply counting the families in the text of the paper that established APG III.
ORDERS: Amborellales (1), Nymphaeales (3), Austrobaileyales (3), Chloranthales (1), Canellales (2), Piperales (5), 
Magnoliales (6), Laurales (7), Acorales (1), Alismatales (13), Petrosaviales (1), Dioscoreales (3), Pandanales (5), Liliales (10), Asparagales (14), Arecales (1), Poales (16), Commelinales (5), Zingiberales (8), Ceratophyllales (1), Ranunculales (7), 
Proteales (3), Trochodendrales (1), Buxales (2), Gunnerales (2), Saxifragales (14), Vitales (1), Zygophyllales (2), 
Celastrales (2), Oxalidales (7), Malpighiales (35), Fabales (4), Rosales (9), Fagales (7), Cucurbitales (7), Geraniales (3), Myrtales (9), Crossosomatales (7), Picramniales (1), Sapindales (9), Huerteales (3), Brassicales (17), Malvales (10), Berberidopsidales (2), Santalales (7), Caryophyllales (34), Cornales (6), Ericales (22), Garryales (2), Gentianales (5), 
Solanales (5), Lamiales (23), Aquifoliales (5), Asterales (11), Escalloniales (1), Bruniales (2), Apiales (7), Paracryphiales (1), Dipsacales (2).
SUPRA-ORDINAL GROUPS: commelinids (1), basal eudicots (1), Pentapetalae (1), lamiids incertae sedis (3), core lamiids (2), angiosperms incertae sedis (2).
The circumscription of the family Icacinaceae remains especially doubtful. "Apodytes" and its close relative, Rhaphiostylis, as well as "Emmotum", "Cassinopsis", and a few other genera were provisionally retained within it until further studies can determine whether they properly belong there.
Three genera ("Gumillea", "Nicobariodendron", and "Petenaea") were placed within the angiosperms incertae sedis. "Gumillea" had been unplaced in APG II. "Nicobariodendron" and "Petenaea" were newly added to the list. The latter was later placed into its own family Petenaeaceae in the order Huerteales
The classification is shown below in two versions. The short version goes to the level of orders and of families unplaced in an order. The detailed version shows all the families. Orders at the same level in the classification are arranged alphabetically. Note that orders may not contain the same families as in earlier versions of the APG system (APG system, APG II system). Further detail on relationships can be seen in the phylogenetic tree below.
Detailed version.
Legend:
† = newly recognized order for the APG system;
§ = new family circumscription described in the text;
$ = families that represent the broader circumscription of options available in APG II and favoured here;
$$ = families that were in square brackets in APG II, the narrower circumscriptions favoured here.
Phylogeny.
The APG III system was based on a phylogenetic tree for the angiosperms which included all of the 59 orders and 4 of the unplaced families. The systematic positions of the other 6 unplaced families was so uncertain that they could not be placed in any of the polytomies in the tree. They are shown in the classification table entitled "Detailed version" above, 4 in Euasterids I and 2 in Taxa of uncertain position.
The phylogenetic tree shown below was published with the APG III system, but without some of the labels that are added here.
Subfamilies replacing discontinued families.
A number of subfamilies have been proposed to replace some of the families which were optional (i.e. bracketed) in APG II, but have been discontinued in APG III. These are shown in the table below.