These lectures explore the application of holography and the AdS/CFT correspondence to condensed matter systems, focusing on quantum phase transitions, transport coefficients, and superconducting/superfluid phase transitions. The first lecture introduces quantum phase transitions, which occur at zero temperature and are driven by quantum fluctuations rather than thermal ones. The second lecture discusses linear response theory and Ward identities, which are essential for understanding the behavior of systems under external perturbations. The third lecture presents transport coefficients derived from AdS/CFT, applicable in the quantum critical region near a phase transition. The fourth lecture extends these ideas to superconducting or superfluid phase transitions using a simple gravitational action. Quantum phase transitions are crucial for understanding phenomena like superconducting-insulator transitions in thin films and high-temperature superconductivity. The quantum rotor model is used to illustrate these transitions, showing how the system changes from a paramagnetic to a magnetically ordered state as a parameter is varied. The lectures also discuss the relevance of AdS/CFT in studying strongly interacting field theories, particularly in condensed matter systems, where it provides a powerful tool for understanding quantum critical points and transport properties. The AdS/CFT correspondence maps strongly interacting field theories to classical gravity, allowing for the calculation of transport coefficients such as viscosity and conductivity. This approach is particularly useful for systems where traditional methods are inapplicable, such as high-temperature superconductors. The lectures highlight the importance of quantum phase transitions in understanding the behavior of materials near critical points, and the potential of holographic techniques to provide insights into quantum gravity through material science or atomic physics. The discussion also includes the Nernst effect in high-temperature superconductors, where a large Nernst coefficient is associated with the superconducting phase transition, suggesting the involvement of non-electronic degrees of freedom like vortices. The lectures conclude with an exploration of Ward identities, which constrain the form of correlation functions and transport coefficients, providing a framework for understanding the behavior of systems under various symmetries and perturbations.These lectures explore the application of holography and the AdS/CFT correspondence to condensed matter systems, focusing on quantum phase transitions, transport coefficients, and superconducting/superfluid phase transitions. The first lecture introduces quantum phase transitions, which occur at zero temperature and are driven by quantum fluctuations rather than thermal ones. The second lecture discusses linear response theory and Ward identities, which are essential for understanding the behavior of systems under external perturbations. The third lecture presents transport coefficients derived from AdS/CFT, applicable in the quantum critical region near a phase transition. The fourth lecture extends these ideas to superconducting or superfluid phase transitions using a simple gravitational action. Quantum phase transitions are crucial for understanding phenomena like superconducting-insulator transitions in thin films and high-temperature superconductivity. The quantum rotor model is used to illustrate these transitions, showing how the system changes from a paramagnetic to a magnetically ordered state as a parameter is varied. The lectures also discuss the relevance of AdS/CFT in studying strongly interacting field theories, particularly in condensed matter systems, where it provides a powerful tool for understanding quantum critical points and transport properties. The AdS/CFT correspondence maps strongly interacting field theories to classical gravity, allowing for the calculation of transport coefficients such as viscosity and conductivity. This approach is particularly useful for systems where traditional methods are inapplicable, such as high-temperature superconductors. The lectures highlight the importance of quantum phase transitions in understanding the behavior of materials near critical points, and the potential of holographic techniques to provide insights into quantum gravity through material science or atomic physics. The discussion also includes the Nernst effect in high-temperature superconductors, where a large Nernst coefficient is associated with the superconducting phase transition, suggesting the involvement of non-electronic degrees of freedom like vortices. The lectures conclude with an exploration of Ward identities, which constrain the form of correlation functions and transport coefficients, providing a framework for understanding the behavior of systems under various symmetries and perturbations.