This foundational mathematics course covers three core topics essential for higher studies in science and engineering. It begins with the principles of Set Theory, Relations, and Applications, establishing the language of modern mathematics through sets, subsets, and logical operations, before defining relations (order and equivalence) and the crucial properties of functions (injectivity, surjectivity, bijectivity). The curriculum then advances to Complex Numbers, introducing their algebraic, trigonometric, and exponential forms, and providing tools to solve polynomial equations and find complex roots. The course culminates with an introduction to Vector Spaces, which lays the groundwork for linear algebra by defining vector spaces, bases, dimension, and the properties of linear applications, including their kernel, image, and rank.