Any number added to 0 makes that number, that is n+0 = n.
Any number multiplied by 0 is 0, that is, 0*n = 0.
Any number to the power of 0 is 1, or in other words, n^0 = 1. And zero to any power is 0, so 0^n = 0. 0 to the power of 0 has an indeterminate value - some people use 1 and some use 0.
x-0 = x, and x/0 is undefined for any x. 0/x is 0, unless x = 0.
Zero represents a quantity of nothing. It is a term in some sequences, often being the 0th term. In addition, some numbering systems in computers start with 0 instead of 1.