What is the true circuit behind an opamp?
Here is a $35 kit you can make, which ends up being the equivalent of a 741 op-amp using discrete 13 2N3904 and 7 2N3906 transistors.  It has eight binding posts representing the eight pins of the device.



Here is a link to the datasheet, which includes the schematic for the kit (shown below) and a BOM.



Compare that to a "real" 741 out of the TI datasheet:



They are virtually the same, even down to the resistor values.

There is also an 11 page "Principles of Operation" which goes into quite a bit of detail on how it works.  And finally, they have a Wiki.