TR1 steps the voltage down
B1 rectifies AC into pulsing DC
C1 filters it (reduces ripple)
IC1 is voltage regulator, it has built in voltage reference (zener), output current sensing and voltage comparator.
Q1 is used to allow large output current (also can be mounted on heat sink)
R3 is small value resistor. it is used to create voltage drop proportional to output current. when this reaches certain limit, (measured by CL and CS pins of LM723) regulator switches to current limiting mode to protect Q1, R3 and circuit.
F2 is there in case current limiting didn't work (maybe Q1 got damaged etc)
R4 and R5 form voltage divider. this is used as feedback to LM723 (measure output voltage and adjust OUT as needed).
C4 is additional smoothing capacitor.
V1 is voltmeter indicating output voltage.
R1, P1 and R2 form reference voltage for +IN (compared with -IN from output)
LM317 is newer voltage regulator and it has built in protection etc.
see
https://www.electro-tech-online.com/custompdfs/2011/07/LM117.pdf for details.
If larger currents are needed, external transistor(s) can be added (see page 17 or 18 for example).
so far discussion was about linear regulator(s). they are simple, can have very low ripple etc but are not suited for large voltage drop.
For example if you want adjustable power supply that can produce 0-30V output, you need input that is at least 33-35V. suppose it is 35V, and you want to power 3A load at 5V output.
this means that 35V-5V=30V drop.
30V * 3A = 90W which is disippated power (converted to heat) so you need massive heatsinks.
This is clearly not efficient, to power 15W load (5V*3A=15W) we had to sacrifice over 90W of power (there are other losses too).
Solution is to use switching power supply. This means adding coil, shotky diode and few more components but we get dramatic improvement in efficiency when voltage drop is significant. Example of switching regulator using LM317 is on page 19 of above link ("4A Switching Regulator with Overload Protection").