This book offers a complete, rigorous review of Linear Algebra, from Vector Spaces to Normal Forms. Emphasizing classical Newtonian treatment (favored by Engineers) of rigid bodies, the text also employs a more modern reliance on Linear Algebra to get inertia matrix and deal with machines. This approach allows uniform treatment of both single bodies in arbitrary axes, and "machines". Analytical dynamics-both Lagrangian and Hamiltonian formulations-are developed to admit non-conservative forces. Throughout, the importance of integrals is emphasized.