The group of natural numbers are those that quantify real objects, therefore they are formed by numbers like 0, 1, 2, 3, ...
The group of integer numbers is the group of natural numbers together with negative numbers, so they are formed by numbers like ..., -3, -2, -1, 0, 1, 2, ...
The group of rational numbers is the group of numbers that can be represented as a fraction. These are numbers like: 1, 2/3, ...