The Opamp is an integrated circuit designed to amplify a signal. It has two inputs,an inverting input (-) and a non-inverting input (+), and one output. An opamp is a differential amplifier, that is it amplifies the difference between the two inputs, a small signal at one input will appear thousands of times (or more) larger at the output. This may not seem very useful at first, to amplify all signals thousands of times, but it all works out. In order to limit the gain of the opamp we use negative feedback. This is a path from the output back to the inverting input (-) to reduce the amplifiers gain. If you were to connect the output directly to the inverting input (-) you would have an amplifier with a gain of +1. In other words the output would look just like the input.
To understand how this works we will analyze what is happening to the differential amplifier. Due to an opamps large gain it will always try to keep the two inputs at the same voltage. As the signal at the non-inverting input (+) raises the amplifiers output will rise, since the inverting input (-) is connected to the output its voltage also rises until the voltage on the inverting input (-) matches the voltage on the non-inverting input (+) (-). In order to make the amplifier have more gain we simply need to show less of the output to the inverting input (-), then the output will reach a higher voltage before the inverting input (-) matches the voltage on the non-inverting input (+). This is easily done with two resistors in a divider. If we divide the output in half then the gain will be +2 if we divide it in tenths the gain will be +10, ect... Gain of a non-inverting amplifier is Gain=(R1+R2)/R2.
There is another way to connect an opamp that will make an inverting amplifier. This means that the output will be the opposite of the input. To make an inverting amplifier just connect the non-inverting pin (-) of the opamp to ground (or any stable voltage) and place the signal through a resistor to the inverting input (-). Remember the opamp will attempt to keep both inputs at the same voltage so the opamp will hold the inverting input (-) at ground (whatever potential the non-inverting input (+) is at.) It can do this by creating a voltage at the output that will cancel the signal voltage. If both the resistors are the same then an input of +1 volt can be canceled by -1 volt at the output, the amplifier has a gain of -1. The gain can be changed by changing the ratio of the divider. The Gain for an inverting amplifier is the negative of the non-inverting amplifiers Gain=-(R1+R2)/R2.
One interesting use of the inverting amplifier is as a signal sum. Since the inverting pin (-) of the amplifier is kept at ground by the amplifier it looks like a resistor to ground for the signal. You could add a second signal resistor to the inverting input (-) and the first signal would know nothing of the second signal. To the opamp it would appear to be one signal, the output would find a voltage to cancel both input signals and therefore sum the two. In fact there is no limit to the number of inputs that you can sum using one opamp. (Note that the sum will actually be a inverse sum, you would need to add a second inverting amplifier after the first to make a normal sum.) You can even adjust the magnitude of each input by varying the value of the input resistors. The gain of the summing amplifier is calculated for each input seperatly Gain=-(R1+R_input)/R_input.
The last amplifier you can make with an opamp is a differential amplifier. This will allow you to amplify only the difference between two signals. It consists of an inverting amplifier with a signal on the non-inverting pin (-). The signal on the non inverting pin (-) must be divided with the same divider used on the inverting side of the amplifier. If both inputs have the same signal on them then the inputs will see the same voltage and there will be no output. If the non-inverting input (+) has the opposite signal as the inverting input (-) then the output will be the difference of the inputs. The differential gain of a differential amplifier is Gain=(R1+R2)/R2.