Parallel and Series Circuits are quite easy to understand. A parallel circuit is one where the wires "diverge" into two or more routes and then come back to one. A series circuit is one where the wires don't diverge and stay in one path. Below is a table which consists of the major differences among voltage, resistance, and current in Parallel and Series Circuits.
Derivations of the resistance equation are obtained by setting I=V/R or V=IR, respectively, due to the Ohm's law (see previous chapter). Since V is constant in parallel and I is constant in series, V and I could be divided by itself in the equation, which consequently gives the total resistance equations. Below is a more "visual" interpretation of the derivation: