Is axis of symmetry considered a true symmetry? In most of the books when i read about optical activity of a compound this is what they say:

A compound that does not posses any kind of symmetry is optically active. In other words chiral compounds without having any kind of of symmetry are optically active.

However, this holds true when we refer to plane of symmetry or centre of symmetry, because molecules having axis of symmetry or alternate axis of symmetry are still optically active.

For example this compound possesses axis of symmetry but is still optically active:

And therefore i am totally confused about relation of optical activity with symmetry.

Thanks for answering the question
A molecule is chiral (1, 2) if it does not have an improper axis of rotation. Since your drawing does not seem to show the meso form of 2,3-dichlorobutane, it is optically active.