The question looks likely to be closed, but here's a start :-
Taking the 'T' attenuator, 'k' represents the reciprocal gain. For example, a required attenuation of 20dB (ie a gain of -20dB) gives a 'k' of 10.
\$Z_0\$ is the required characteristic impedance of the circuit into which the attenuator is to be placed. With a source impedance of \$Z_0\$, the output impedance of the attenuator will also be \$Z_0\$, and with a load impedance of \$Z_0\$, the input impedance will also be \$Z_0\$. The calculated attenuation will only be achieved with this source and load impedance. The resistor values are derived from three simultaneous equations for gain, input impedance and output impedance.
For the 'L' pads things are different since the source and load impedances cannot be the same. For the first pad, with a matched load impedance, the input impedance will also be matched. However, even with a matched source impedance, the output impedance will not be matched.
The second 'L' pad is similar but allows the output impedance to be matched at the expense of the input impedance.
I haven't checked the formulae for the other pads but it's all just Ohm's law, KVL & KCL from there.