Yes, tennis is a part of the Olympics. It appeared first in the 1896 summer Olympics in Athens, Greece but tennis was dropped after the 1924 summer Olympics in Paris, France due to a disagreement between the International Olympics Committee and International lawn tennis federation.
Tennis appeared in Olympics as a demonstration sport from 1928 to 1984, expect for 1968 olympics where it was played as a full medal sport. Tennis officially resumed Olympics as a full medal sport in 1988 summer Olympics in Seoul, South Korea and it has remained a part of the Olympics since then up to the last Olympics in 2016.