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Geometric Quantum Mechanics is a novel and prospecting approach motivated bythe belief that our world is ultimately geometrical. At the heart of that is aquantity called Quantum Geometric Tensor (or Fubini-Study metric), which is acomplex tensor with the real part serving as the Riemannian metric thatmeasures the `quantum distance', and the imaginary part being the Berrycurvature. Following a physical introduction of the basic formalism, weillustrate its physical significance in both the adiabatic and non-adiabaticsystems.

Quantum Geometric Tensor (Fubini-Study Metric) in Simple Quantum System: A pedagogical Introduction