Pump-probe spectroscopy is a versatile and powerful technique to probe the microscopic dynamics of energy carriers. This course is designed to give a clear picture of pump-probe spectroscopy for the study of phonons in nano- to micron-scale. We will cover fundamentals of related fields including lasers, optics, photonics and technical knowledge to understand working principles and underlying physics of various pump-probe spectroscopy experiments, which have been a great success in the territory of the studies on heat transfer. By solving analytical models and applying data processing methods, we show that pump-probe spectroscopy techniques have successfully measured various types of materials and structures, discovered non-conventional thermal transport in materials and provided unique opportunities building the foundation of modern thermal science.