This chapter builds upon the foundational single degree-of-freedom (SDOF) vibration model by introducing the more comprehensive multi degree-of-freedom (MDOF) representation. MDOF systems more accurately model dynamic structures using multiple masses and rigid bodies connected through elastic and dissipative elements. These advanced models incorporate the core SDOF concepts of natural frequencies and damping coefficients, while also introducing the important concept of spatial modes of vibration. Mathematically, the dynamic behavior is governed by a system of coupled, second-order, simultaneous differential equations, the solution of which is obtained applying the linear algebra principles of eigenvalues and eigenvectors.