Firstly, there are many different kinds of transistor. for example: BJT, JFET, MOSFET, IGBT, ESBT and SIT.
Of course circuits can be made without transistors. Some circuits like power supplies and crystal radios can be made using only passive components like transformers, capacitors, inductors, diodes and resistors.
Other circuits use different kinds of semiconductor active devices. Light dimmers use triacs. Amplifiers and oscillators can be made with Tunnel diodes or Gunn diodes.
Before transistors and other semiconductors were invented, thermionic valves were widely used. They are still sometimes used today in things like radio transmitters and guitar amplifiers.
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IIRC, you are pursuing a master's degree in VLSI. I am surprised you did not learn basic electronics first.