Can light absorb energy? Everybody knows that all physics systems absorb light quanta, any material thing can absorb light quanta. But the reverse question is , can light absorb energy and therefore changes its frequency? If not, please give me some fundamentals or equations that prohibit this from  happening.
 A: The process of inverse Compton scattering does exactly this. A photon can interact with a relativistic (ie. hot) electron, absorbs some of its energy, and emerges from the interaction with a higher frequency and energy. This has the effect of cooling the electrons. Roughly speaking, the new frequency is related to the original frequency by $\nu \sim \gamma^2 \nu_0$, where $\gamma$ is the Lorentz factor of the electrons.
In astrophysics, this process can be an important source of very high energy photons (e.g. the interaction of radio waves with ultrarelativisic electrons in jets from active Galactic nuclei) and thus a significant cooling mechanism. An interesting piece of trivia is that because of inverse Compton scattering with cosmic microwave background photons, the maximum "lifetime" of any relativistic electron is about $2\times 10^{12}/\gamma$ years.
A: As you say, light is composed of quanta, and they are called photons. They are elementary particles and they have energy h*nu . They can be generated by changing charges and magnetic fields, by the atomic transitions from excited energy levels.
For an observer at rest with respect to the atoms  (or accelerating charges) emitting the photons  the energy they have is given by h*nu where nu is the frequency of the classical electromagnetic beam that emerges from the synergy of innumerable similar photons. If the source is in motion versus the observer then energy of the photon changes either red shifted ( moving away) or blue shifted ( coming towards).
So to change the frequency of photons, and therefor light, one has to start moving, i.e. expend energy, either towards or away from the source of light. When the change  in frequency is positive the particular photon has absorbed the energy given by the relative motion between two inertial systems, for negative it has lost energy.
This has been used in Laser cooling:

Starting in about 1985 with the work of Steven Chu and others, the use of lasers to achieve extremely low temperatures has advanced to the point that temperatures of 10^-9 K have been reached. If an atom is traveling toward a laser beam and absorbs a photon from the laser, it will be slowed by the fact that the photon has momentum p = E/c = h/λ. If we take a sodium atom as an example, and assume that a number of sodium atoms are freely moving in a vacuum chamber at 300K, the rms velocity of a sodium atom from the Maxwell speed distribution would be about 570 m/s. Then if a laser is tuned just below one of the sodium d-lines (589.0 and 589.6 nm, about 2.1 eV), a sodium atom traveling toward the laser and absorbing a laser photon would have its momentum reduced by the amount of the momentum of the photon. It would take a large number of such absorptions to cool the sodium atoms to near 0K since one absorption would slow a sodium atom by only about 3 cm/s out of a speed of 570 m/s. A straight projection requires almost 20,000 photons to reduce the sodium atom momentum to zero.

