Ammonites are part of the phylum Mollusca (along with gastropods, nautiloids, octopus and many other groups). More specifically they belong to the cephalopoda class. They arose during the Devonian, and became extinct at the end of the Cretaceous. They are particularly useful as biostratigraphic markers as they evolved rapidly - individual genera lasted only short periods geologically speaking.
This specimen displays the classic differences with gastropods from the same phylum. Ammonites have a bilateral symmetry because they coil within the same plane rather than a helical shape like gastopods (no symmetry). Also unlike gastropds (snails), ammonites also abandoned onder sections of their shell as they grew, which then became buoyancy chambers - they were free-swimmers like nautiloids, unlike gastropods which are benthic.