gain in an op-amp is the output voltage divided by input voltage.
for the inverting amplifier , gain(Av)=-(Rf/Ri) ,where Rf => resistance of the feedback path & Ri=> inverting input terminal resistance
for the non-inverting amplifier , gain(Av)=(1+(Rf/Ri)) , where Rf => same & Ri=> non inverting input terminal resisance
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In an op-amp, an input on the inverting terminal drives the output in the opposite direction, while an input on the non inverting terminal drives the output in the same direction. In a normal closed loop negative feedback configuration, there is feedback from output to inverting input, so that the output becomes a known function of input. So long as you stay within limits, the output will go to whatever value is required to make the inputs be the same.
A practical opamp is designed to approach the characteristics of the ideal opamp as closely as possible. The open loop voltage gain of an ideal opamp is infinite, so while this is actually impossible to achieve practical opamps are built with as high an open loop voltage gain as possible.
741 opamp
An opamp buffer circuit is one where the input signal is connected to the plus input, and the output is connected to the minus input. Within the performance limitations of the opamp, the output will track the input. The advantage of the buffer circuit is that is presents very little load impedance to the input signal, while providing a low impedance from the output to drive whatever circuitry is connected there.
Possibly Linear, in which case it means analog. The LM324 is an opamp.