This lecture provides an introduction to the theory of homogeneous and heterogeneous germination, focusing on the significance of nucleation in materials science. It discusses the impact of germination on grain size, particularly in aluminum alloys, where the addition of grain refiners like TiB₂ and Ir can drastically alter grain structure. The instructor explains the processes involved in achieving fine grain sizes, which are crucial in industries such as watchmaking. The lecture also covers the Czochralski process for growing single crystals, emphasizing the importance of grain size in microelectronics. Additionally, it addresses the challenges of avoiding crystallization in bulk metallic glasses (BMGs) and the conditions necessary for their formation. The theory of germination is explored, including the concepts of clusters and the critical radius for nucleation. The lecture concludes with a discussion on the interfaces between solid and liquid phases, highlighting their role in the solidification process and the implications for material properties.