If you could really care less about the theory behind op-amps or just don't want to read right now, skip this step. There won't be any heavy math involved, just some summarizing. I recommend you take the time at some point to read up on them though since they are so useful in so many applications. Some really good educational/instructional material is available here, under Chapter 5.

Op-amps are usually two-input, one-output devices, with additional pins for +/- voltage supplies. By looking at the difference between the two inputs, and using the +/- voltage supplies as max/min output values, the op-amp will output a voltage reference value that can be many times higher than the input. The value of amplification is called the gain and is often seen measured in decibels (dB). Regardless of what you are amplifying, be it voltage, current, or power, dividing the output by the input will give you your overall gain. Different op-amp designs have different maximum values that they can achieve for the gain, but for the vast majority of applications, you get to choose the level of gain you want to apply to the input differential. You can also choose to have the output be the inverse of the input or match the input. The inputs are labeled "inverting" and "non-inverting" and there are two equations to determine the gain value of your op-amp design, one for a non-inverting configuration and the other for an inverting configuration. Note that for the non-inverting equation, you have an additional gain of 1 that you can't avoid. If, for example, you connect the non-inverting pin to GND and the inverting pin to your signal, the output will be phase shifted by 180 deg and amplified by the gain. On a graph, it would be completely flipped upside down over the x-axis (see image 2). If you switch the inputs and connect the inverting pin to ground and the non-inverting pin to your signal, the output will look just like the input (see image 3).

Op-amps typically have an extremely high gain built in by default which you the user cannot change, and if you don't design feedback into the system, you'll saturate the op-amp very quickly and hit one of the voltage supply rails. That implies that an op-amp with no feedback will function as a comparator, meaning that if there is a difference in voltage between the two inputs (+ or -), even by the tiniest amount, the output will match the value of the corresponding supply voltage rail. In logic terms, you get a 1 or 0. This can be useful in certain applications, like generating a square wave from a sine or triangle wave, but not in all cases. Many times you want the output to be a scaled version of the input, identical except for magnitude. In order to control the gain, you must implement feedback, connecting one input or the other to the output through one or more passive components like resistors, capacitors, or inductors.

Some applications of op-amps include voltage buffers/followers, low-, high-, and band-pass filters, comparators, integrators, differentiators, peak detectors, voltage/current regulators, and analog-to-digital converters and digital-to-analog converters. I will be going over some of these uses in later steps.

Op-amps also come in many, many different design options, so choosing the right one can be difficult. Should you use an OP37 or LM741? You decide you want really high speed, so you choose the OP37. But which version? The OP37A, C, E, F, G, N, NT, GT, or GR? Will you need more than one in your design? If so, should you use singles, duals, or quads? Of course each one has it's own datasheet, so it can be difficult to do comparisons easily. Just to give you an idea, I've included an Excel spreadsheet with just a few parameters listed to show the wide range of ICs available. It is not an exhaustive listing of all specs, just some basic data.

By comparing some of the data, we can see that the 741 op-amp is not very high speed (low slew rate), nor does it have a high gain-bandwidth product (GBP). The OP37 however has a much (much, much) higher slew rate and GBP, so it can be used over a much wider range of frequencies than can the 741. The other ICs all fall somewhere in the spectrum of speed vs reliability vs... whatever else you want to compare. Each one has it's own application, and it's up to you to decide how you want to use it. For most applications though, pretty much any op-amp will work. If you are designing something that is on the extreme end (e.g. high speed, high voltage, high gain), look through the datasheets to find the one that best suits your needs. As mentioned, I will be showing some simple op-amp circuits that can be built with any of these chips, but there will be some points where I point out the strengths/weaknesses of certain chips. For more information about op-amps, see this website.