English
The periodontium is the part that supports your teeth.
It is comprised of 4 different hard or soft tissues:
. gum
. cementum
. periodontal ligament
. alveolar bone
As for your teeth, these are comprised of a crown (visible part) and of a root; the region between the crown and the root is called the neck.
The crown is made up of:
. enamel that covers the entire crown
. dentin that, visible through the enamel by transparency, gives the tooth its colour
. pulp, the living part of the tooth as shown by its wealth of nerves and blood vessels.
The tool also comprises the dentin and root, but is covered by cementum.

Gum
The gum is part of the buccal mucosal and constitutes the visible part of the periodontium. It surrounds the tooth necks and covers the alveolar bone. The edge of the gum covers the enamel, without being attached to the tooth (if is affixed by simple adherence), thus leaving a space between the tooth and the gum, called gingivodental crevice.
Cementum
The cementum is both part of the tooth and of the periodontium. It is an essential element serving to anchor the tooth. The cementum also protects the roots. It is similar to bone, though it contains neither blood vessels nor nerves.
Periodontal ligament (alveolodental ligament)
The ligament ensures the attachment of the tooth in the alveolus (cavity in which the tooth sits) by means of connective tissue surrounding the root.
The periodontal ligament inserts, on the one hand into the alveolar bone and, on the other hand, into the cementum. In this manner, the tooth is not welded to the bone.
Alveolar bone
The alveolar bone surrounds the tooth and holds it in place. When the tooth is no longer in place, the alveolar bone is progressively rebuilt and absorbed. The alveolus (cavity in which the tooth sits) only exists by virtue of the presence of the tooth it surrounds.
References :
Wolf HF, et al. Parodontologie.3rd Ed. Paris, Masson; 2005. p. 7-20.
Bercy P. Le parodonte sain et ses modifications histopathologiques. In Bercy P, Tenenbaum H. Parodontologie, du diagnostic à la pratique. 1st Ed. Bruxelles, De Boeck Université; 1996. p. 13-23.
Cymes M, Hescot P. Vos dents : Qui, quoi, combien? Tour, Balland/Jacob-Duvernet; 2001. p.5-18.
Lézy JP, Princ G. Pathologie maxillo-faciale et stomatologie. Abrégés. 3rd Ed. Paris, Masson: 2004. p.47-94.