The Java programming language includes five simple arithmetic operators: addition (+), subtraction (-), multiplication (*), division (/), and modulo (%). It also includes unary operators like increment (++), decrement (--), negation (!), and complement (~). Comparison operators return a boolean and include <, <=, >, >=, and instanceof. Assignment operators assign values to variables. Shift operators (<<, >>, >>>) perform left and right bitwise shifts on integral data types.