As the basic laws to solve any circuit/network are KCL and KVL but in some cases it is very hard to solve the circuit using these two laws then we go for some methods/theorems, they are 

1. Voltage and Current Division Rule

2. Superposition Theorem

3. Thevenin’s Theorem  

4. Norton's Theorem 

5. Nodal Analysis

6. Maximum Power Transfer Theorem 

Voltage Division Rule - 
Voltage division rule states that the voltage applied across a series connection of multiple resistors is divided among the resistors in proportional to their resistance. i.e. the voltage drop will be maximum across the resistor having maximum value of resistance.

 
V = V x Rn/R1+R2+....+Rn

Current Division Rule - 
Current division rule states that the total current divided in parallel combination of two resistance is inversely proportional to the value of resistance. This rule is to tell us the current is divided in parallel connected resistance and is applicable for AC and DC circuits. Also the rule should not be applied when the number of resistance in parallel is more than two.

IRn = I x Rn/R1+R2+....+Rn
   

Superposition theorem

• The theorem states that, a circuit with multiple voltage and current sources is equal to the sum of the simplified circuits using just one of the sources.

• In other words, the total response of a linear network is identical to that found by considering each voltage source alone with all other sources removed and replaced by short circuits and then summing the individual responses.