The human species has the follow classification :
Domain :Eukarya
Kingdom :Animalia
Phylum Chordata
Class :Mammalia
Order :Primates
Family :Hominidae
Genus :Homo
Species :sapiens
Therefore, mammalia presents the class in which humans belong along with other mammals like elephants, tigers etc.
Hominidae is the family in which humans and our ancestors and close relatives are classified.