It is unclear, from the schematic what exactly your circuit is supposed to do and what the intended inputs and outputs are. Can you clarfiy what you are trying to accomplish?
It seems you are trying to implement the UC3842 Reference Schematic for a offline SMPS based on a current mode PWM controller, the datasheet for this part is 60 pages and has many details that are impossible to review without more thorough documentation on your side. At the bare minimum many of the capacitor and resistor values can be chosen only when certain details like output voltage, input voltage, and expected load, is known.
Additionally, as @ohazi pointed out, all of your components are lacking ratings and specs. Most, if not all of the difficult engineering (“real engineering”) will be in specifying the exact rating and specification of all the components, like transformers, chokes, and diodes. So please elaborate, otherwise the schematic is quite incomplete at this juncture. An incomplete copy of the reference schematic only serves to diminish your learning of electronics (in my opinion)
Switching Supplies have many caveats, and the reference implementation is just a reference, it is incomplete for most purposes and needs to be adapted.
AC/DC power supplies are extremely inexpensive and use highly optimized, safe, and verified designs. Academic curiosity has it’s place, but from a purely engineering perspective you are reinventing the wheel, somewhat, but you are starting not from a normal wheel, but a formula-1 wheel and trying to reverse engineer.
I would highly suggest you refocus on implementing a DC/DC SMPS supply using a different current mode controller. It shares many of the same design challenges, but you do not have to worry about Mains isolation and is much safer. If you have a risky side, and simply want to work with AC voltages, I would highly suggest instead a simpler, traditional transformer and rectifier based ac supply (like the one @ohazi presents)
If you do choose to implement this circuit. Please use an AC power supply and do not plug into the wall.
This component is a common mode choke, and not a transformer, it is connected correctly for its purpose (to filter high frequency transients from the supply line). The rectifier is connected per the reference design, which is not traditional configuration because this is an offline (online? whatever, riding on mains) supply arrangement.