This is a first-year course which is part of a sequence of two consecutive courses. In this course, we will cover the following topics in Linear Algebra: Determinants, eigenvalues, eigenvectors, and diagonalization, canonical forms, and inner product and norm, Gram-Schmidt process. If time permits, we will also cover topics among the following: adjoint of a linear operator, normal and self-adjoint operators, unitary and orthogonal operators, spectral theorem. The language and concepts of matrix theory and, more generally, of linear algebra have come into widespread usage in the social and natural sciences, computer science, and statistics. In addition, linear algebra continues to be of great importance in modern treatments of geometry and analysis. Nowadays, Linear Algebra is one of the pillars of data science and machine learning.