Master the bedrock of modern mathematics. This course provides a rigorous introduction to set theory, the fundamental language used to structure nearly every mathematical discipline. We move quickly from defining basic sets and elements to complex operations including unions, intersections, and complements. You will analyze relationships between collections using Venn diagrams, master set-builder notation, and examine the properties of power sets and Cartesian products, establishing the ground rules for all subsequent mathematical study. Mathematical rigour is essential for advanced problem-solving. Set theory is not abstract trivia; it is the critical organizational framework underpinning computer science database structures, logical reasoning systems in artificial intelligence, and complex data stratification in statistical analysis. Fluency in set operations allows you to define precise categories, manage data relationships efficiently, and construct watertight logical arguments required in professional technical environments. Upon completion, you will possess the skills to define sets accurately using various notations and execute operations on finite and infinite collections with precision. You will demonstrate competence in proving fundamental set identities, manipulating Venn diagrams to solve practical problems, and formalising relationships between distinct data groups. Furthermore, you will establish the foundational understanding of relations and functions necessary for progression into advanced calculus and abstract algebra. This course is targeted at students entering undergraduate foundation programmes requiring strong quantitative proficiency, particularly in mathematics, computer science, and engineering. It also serves as an intensive structural refresher for professionals shifting into data-architecture or analytical roles demanding strong logical literacy. Prior exposure to standard secondary school mathematics is assumed; focus is placed strictly on mastery and application of rigorous definitions.