Explore quantum phase transitions through two comprehensive lectures focusing on the Transverse Field Ising Model and path integrals in quantum phase transitions (QPT). Learn advanced concepts from the 4th Vignayana Patashala series on Phase Transitions and Renormalization Group, delivered at the Raman Research Institute. Delve into the theoretical foundations and mathematical frameworks used to understand quantum systems undergoing phase transitions, with particular emphasis on the application of path integral methods in analyzing quantum phase transitions.