Computer instructions can be classified into three categories: data transfer instructions, data manipulation instructions, and program control instructions. Data transfer instructions move data between locations without changing it. Data manipulation instructions perform arithmetic, logical, and shift operations. Program control instructions provide decision-making and allow changing the flow of a program. Common data transfer instructions include load, store, move, exchange, input, and output. Arithmetic instructions perform addition, subtraction, multiplication, and division. Logical and bit manipulation instructions perform AND, OR, and XOR operations on bits. Shift instructions move bits left or right. Program control instructions include branch, jump, skip, call, and return.