Linear convolution is a mathematical operation. It is done to calculate the output of any Linear-Time Invariant (LTI) system given its input and impulse response.
Circular convolution, also known as cyclic convolution, is a special case of periodic convolution, which is the convolution of two periodic functions that have the same period.
In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other.
Auto correlation measures the relationship between a variable's current value and its past values.