These lecture notes are the legacy of the training schools of the COST Action CA23130 “Bridging high and low energies in search of quantum gravity” (BridgeQG). Their central theme is the complementary exploration of quantum gravity (QG) across vastly different energy scales. With the rapid development of quantum technologies, it is becoming increasingly feasible to search for quantum-gravitational effects not only in the highest-energy physical systems, such as cosmic messengers including gamma rays, neutrinos, cosmic rays, and gravitational waves, but also at low energies through ultra-high-precision laboratory experiments involving matter-wave interferometers, atomic clocks, qubits, and entanglement-based setups.