Learn the mathematical technique of bosonisation through this comprehensive physics lecture that transforms fermionic systems into equivalent bosonic representations. Explore the fundamental principles behind mapping fermionic operators to bosonic fields, understand the mathematical framework that enables this transformation, and discover how bosonisation provides powerful analytical tools for solving strongly correlated quantum many-body systems. Examine specific applications in one-dimensional quantum systems, including the treatment of Luttinger liquids and spin chains, while mastering the technical details of operator mappings and correlation function calculations. Gain insights into how this technique bridges different theoretical approaches in condensed matter physics and quantum field theory, making complex fermionic problems more tractable through bosonic methods.