This dissertation investigates the structure and behavior of two-dimensional (2D) pancake vortices in a stack of N Josephson-decoupled superconducting thin films under a magnetic field applied prependicular to the layers. This system of magnetically coupled superconducting films is proposed as a model for the multilayered high-Tc superconductors. Starting with the properties of one pancake vortex located in any of the N superconducting layers, an analytical expression is derived for the magnetic coupling force between pairs of 2D pancake vortex lattices residing in different layers, each having the same lattice structure, but displaced (not rotated) relative to each other. Using this expression, N triangular pancake vortex lattices are studied under the action of equal but oppositely directed applied currents flowing in the top and bottom layers. In this first study, pinning in the superconducting layers is taken to be negligible. This is then followed by an investigation of the dynamics and current-voltage characteristics of N such pancake vortex lattices when transport current flows only in the top layer. Both zero and nonzero uniform pinning are considered in this second study. In both situations, however, it is found that a pancake vortex lattice residing in an outer plane carrying transport current becomes magnetically decoupled from the other layers when the magnitude of the applied current is greater than a certain decoupling value. This decoupling surface current density is calculated for different values of the applied magnetic field, the critical surface current density associated with pinning, and total number of layers N.