Two of the most common are series connections and parallel connections. Resistors are in series if they carry necessarily the same current. Current flows from one series resistor into the next with no alternative paths. We can replace a series combination of resistors by a single resistor which carries the same current as the series branch and which supports the same total potential difference. The equivalent resistance to a set of series resistances is the sum of the resistors.
Resistors are in parallel if they support the same potential difference.
The equivalent parallel resistor also supports that same potential difference but produces the current which is the sum of the parallel currents. Thus the reciprocal of the equivalent parallel resistance is the sum of the reciprocal resistance of the parallel elements. The conductance of the equivalent resistor is the sum of the individual conductances in the parallel elements.