Two laws by Kirchoff are commonly used in circuit analysis. The first is known as Kirchoff's current law, and the second one is Kirchoff's voltage law.
Kirchoff's Current Law
Kirchoff's Current Law states that the sum of the currents entering a wikt:node (the point where two or more circuit elements meet) is equal to zero, with the understanding that current flowing out of a node represents a negative number. An equivalent statement of the law is that or the sum of all currents leaving the node equals the sum of all currents entering the node. This law is in fact a statement of the conservation of charge in a circuit.
Kirchoff's Second Law
Kirchoff's Voltage Law states that the sum of the voltages\potential differences in a loop or mesh equals zero. This law is a statement of the conservation of energy, because 1 volt represents the energy associated with one unit of charge passing through that point.