Conservation law is a physical law that says that some physical quantity is conserved, which means never changes. Examples of conserved quantities in physics are energy and momentum along 3 axes. So we have at least 4 independent conservation laws of momentum along axis 1, momentum along axis 2, momentum along axis 3, and energy, that is considered axis 4 by some authors or axis 0 by others. Usually mathematicians use different convention for numbering axes than physicists, who number axes starting from 0 for energy, and so on for other axes (e.g. t, x, y, z where t denotes time, and the rest relate to space).