What is “Sensitivities” or "Greeks" in market finance?

Suppose that we have a financial derivative (example: Option) associated to an underlying asset (example: Stock).

Then the price “V” of this derivative will depend mainly on two factors:

• The price “S” of the underlying asset,
• The (implied) volatility “Sigma” of the underlying asset,
• plus, other factors, but with less impacts.

The “sensitivities” measure the impact of these factors (“S” & “Sigma”) on the derivative price. They are often designated by “Greeks” letters, and defined mathematically as follows:

Share other sensitivities and their purpose?? !