We restrict our study to the properties of LTI systems
Linearity
A system is said to be linear if it satisfies the principle of superposition.
Superposition=Homogeneity+Additivity
Time Invariance
If 
Time invariance implies 
Some other properties of systems :
Causality
In a causal system the output does not precede (in time) or anticipate the input.
Stability
Stability requires that a finite system input produces a finite system output.
An example of an unstable system could be a high gain linear amplifier with
positive feedback.