This course is part I of a series of courses. It offers a rigorous introduction to linear algebra, guided by the foundational textbook by Gilbert Strang. Designed for students with a keen interest in mathematics and its applications, the course focuses on the core concepts presented in the first four chapters of Strang's book, while enhancing the learning experience with a comprehensive set of lecture notes that include all necessary proofs, which go beyond what is provided in the textbook.

The course emphasizes a balanced approach, combining mathematical rigor with intuitive understanding. Key topics include systems of linear equations, vector spaces, and orthogonality. Students will not only master the theoretical aspects of these subjects but also develop a strong intuition for their practical applications in various fields.