Hi, did i explain the role of each components well in this amplifier circuit ?

[nyame]

Hi, please did i explain the role of each component correctly in this amplifier circuit, and please some one should also reference a book for me were i can learn more about this topic

[Nitrousoxide]

Resistor 8.2kΩ and resistor 2.3kΩ act as a resistive divide to hold the base
voltage constant at a designated point, the voltage divider centre point
holds the base at a DC potential just above the required base emitter
junction bias voltage of 0.6 or 0.7 for the BC108 transistor

The BJT is fundamentally seen as a current controlled current source in black box form. It is because the base emitter junction is forward biased, that the voltage drop is the same as a PN junction drop. Thus the voltage present on the base pin only need to be higher than this to forward bias the diode (depending on desired operation mode, you may not want this). This can be seen through the use of other biasing techniques that use a single resistor tied to (usually) the positive supply to provide a fixed current.

The collector resistor sets a limit of the collector current and also the
loading impedance for the transistor to develop a voltage swing across. It
also sets the loading line output swing to the minimum and maximum
values; it sets the maximum power dissipated in the collector of the
transistor, the 20kΩ resistor is use to take out DC from the capacitor.

As previously mentioned the device can be modelled as a current controlled current source and thus when current passes through a resistor a voltage drop (or differential) is formed, this is the output voltage. It does not limit the collector current, the steady state collector current is a function of biasing (and maximum current gain). The resistor seems to simply be an output load.

If you want to find the correct formula for the output/input impedance, you can refer to small signal models for BJT's.

The emitter resistors 460Ω, 607 and 22uf capacitor create a network that
is use for thermal stability of the base emitter junction, it help in addition to
control the over voltage gain and bias current through the transistor, it
values also effect the input and output impedance.

I wouldn't say emitter degeneration is for thermal stability. Again, this is where one equation can speak 1000 words. Derive/prove the correct formula and it should be self explanatory (or with the addition of a justification, much easier to explain).

The transistor is the active device amplifying the source signal; the battery
supplies the DC power to the circuit.
The two coupling capacitors set the lowest frequency roll off of the circuit,
while also isolating the output and the input from DC effects of their earlier
and later stages.

Yes, the input and output capacitors are for DC coupling.

Microelectronic Circuits by Sedra Smith is a good textbook.