Does light have mass?
Short answer: no.
Light does not have mass.
However, light does exhibit some important properties that you might relate to something with mass. Some examples are
If we model light as a stream of particles (photons) then the photons carry a momentum that can change the photon's energy into kinetic. If the wavelength of the photon is known then it's momentum is given by:
Affected by gravity.
Although massless light is still affected by gravity. This easily seen by the fact that light can't escape a black hole because the black hole's gravity is so strong. It can also be seen through gravitational lensing.
Despite these properties light is for all intents and purposes massless. By Einstein's theory of relativity, in order to travel at the speed of light, you require an infinite amount of energy or the thing travelling at the speed of light must have no mass.