1: A op-amp can be modified to do different things. For instance, it could be modified into a summing amplifier who does addition. But, is there anything in itself such as op-amp? What does it do? Or, is it simply a catch all term for all related amplifiers such as differential amplifier, summing amplifier, etc.?
An op amp is a differential amplifier circuit made of of multiple transistors. This basic device can be modified to perform a particular task by adding resistors, caps, and inductors around it in specific configurations, depending on the task you want it to perform. For instance, two resistors can make it into an inverting amplifier with user-selectable gain. Add another resistor, and you can make a non-inverting amplifier. Add a capacitor, and you can make a voltage integrator.... the list is extensive. See the App Note I pointed to earlier for the many circuits that you can build, using an op-amp as the basic building block.
2: Are there other kinds of amplifiers besides op-amp?
An op-amp is actually a collection of several different circuits, including amplifiers and current mirrors (simple transistor-based circuits). A very basic (fundamental) amplifier is constructed using a single transistor. For more information, fire up your favorite search engine (or search on here) for Class A amplifiers. Simple transistor amplifiers are the fundamental building blocks of all the electronic circuits we use today. The two major ways that a transistor is used are: as an amplifier, or as a switch (on/off).
Here's what's inside a 741 operational amplifier:
**broken link removed**
3: I have always been under the impression that an amplifier is used to amplify voltage. Can an amplifier also be used to amplify current?
Yes, kinda... it's not quite like what you might be thinking of knowing what an op-amp is, but search for current-mode amplifiers. This is a higher-level subject than I think we should get into in this conversation. Once you get past class A amps and start looking at other non-linear types, you will see current-mode amplifiers show up. You can set up an op-amp to convert a current signal into a voltage, but that's not the 1:1 correlation that you originally asked about.
4: The word 'feedback' simply suggests something that is returned to a machine, system, or process to improve output. I have seen in some circuits that a wire connects the output of the amplifier with one of its input and I presume it's called feedback. How would you explain this feedback and its use? Please keep it simple.
Feedback is a general term used in system design. The op-amp, and it's surrounding circuits, can be considered a system. This system can be expressed as a series of simple equations that define output voltage, based on the input voltage and the output voltage (thus feedback... some of the output voltage is sent back to modify the input voltage).
For a simple way to understand how an op-amp works, it always tries to make the + and - inputs stay at the same voltage, by changing the output voltage. Let's say you set up the circuit as a simple inverting op-amp. You apply 0 volts to the + input. Assume that the input resistor and feedback resistor are both 1Kohm. If you apply +1V to the input resistor, then the output of the circuit will go to -1V. Why?
Remember that the op-amp will change the output voltage so that the + and - inputs are the same voltage. If + is 0V, then - must also become 0V. If you have 1V at the input resistor, then some quick calculations with Ohms law (V=I*R) will tell you than the output voltage must be -1V, so that the - input is 0 volts. One thing to keep in mind, when solving equations around an op-amp, you assume that the input pins have zero current going into, or out of, them.