Is Invisibility possible according to physics? Is there any backing theory to prove it true or false?
This is an active area of research in both optics and acoustics using diffractive elements.
You can think of these diffractive elements as guiding all the incoming light around them, thus reproducing the input radiation at the output, resulting in invisibility. The are often referred to as "cloaks."
The current reason why they don't work in practice is because they have only been shown to work at specific wavelengths (or colors), and not over a wide band of wavelengths simultaneously.
See this Wikipedia page for more details.
Yes it is possible
If the object has the same refractive index as a surrounding fluid it is not visible.
If the object does not produce or reflect light (such as a black hole) it is invisble.
complex systems are being produced to create nanoscale invisible objects now.