Circuit elements are connected in series when a common current
passes through each element.
The equivalent resistance 
of a combination of resistors
connected in series is given by summing the voltage drops across
each resistor.
If 
, where 
are all the other resistors than 
; the largest resistor wins.
Circuit elements are connected in parallel when a common voltage
is applied across each element.
The equivalent resistance of a combination of resistors
connected in parallel is given by summing the current through
each resistor
If 
, where are all the other resistors than
; the smallest resistor wins.
The following ``divider'' circuits are useful combinations of resistors. Believe it or not, they are a super useful concept that will often be used in one form or another; learn it.