These are excellent are rigorous lecture notes in Linear Algebra for junior undergraduate mathematics students which covers all standard topics in such a course (from vector spaces, linear operators, matrices, systems of linear equations and determinants, to normed vector spaces and multilinear forms). All theorems are stated with proofs ! This material can be recommended to all who wish to obtain a good knowledge of fundamentals of linear algebra, needed for other undergraduate courses (like multivariable calculus, differential equations, functional analysis, optimisation…).