Schmitt Trigger
This looks like a non-inverting amplifier with the inputs hooked up backwards.
How it works. The output has two levels, either saturated positive or negative. This is a digital circuit output. The input can be any value. Thus the schmitt trigger can be used to change a signal from analog to digital or remove noise from a digital signal.
To see how the output changes as the input changes (Assume the op-amp saturates at +15 and -15 V. Assume both resistors are equal.) start with the output at +15 V. The positive input will be +7.5 V. Since the output is saturated positive the negative input must be less than +7.5 V. Thus if the input Vi is less than 7.5 V the output will remain at +15 V.
Raise the input above 7.5 V and the output will saturate negative at -15 V. The positive input will now be -7.5 V. Since the output is saturated negative the negative input must be greater than -7.5 V. Now if the input Vi is greater than -7.5 V the output will remain at -15 V.
In theory, the output could be twice the input. But this is unstable and any change in the input will cause the output to go to saturation. If the input increases a little the output decreases more and so does the positive input making the output decrease more till the output saturates negative.